For all the world this looked destined to finish scoreless. Then up stepped Gylfi Sigurdsson with a captain's contribution to send Everton above Manchester United and Leicester City into second positon.
The apparently inevitable stalemate wasn't for want of trying from Everton. Dominic Calvert-Lewin improvised brilliantly for one first-half effort and Alex Iwobi's running and creativity caused Sheffield United problems.
But Aaron Ramsdale hadn't been fully extended, albeit the home goalkeeper had watched a Sigurdsson strike fizz past his upright.
Then, with 10 minutes remaining, Sigurdsson again.
Bernard, on for Anthony Gordon, cushioned a ball falling from the sky, the Brazilian's touch easing possession to Abdoulaye Doucoure.
Midfielder Doucoure's presence in the heart of the box spoke to Everton's ambition and he funnelled the ball on to Sigurdsson, who landed the decisive blow with an angled strike from 10 yards.
Everton have won four successive Premier League matches for the second time this season, the first time they've achieved that since winning the Club's ninth league title 33 years ago.
They have won five of their opening top-flight away matches, too.
Everton had most of the ball from the outset but Sheffield United, with their blanket five-man backline, represent a conundrum for their opponents.
The Blades are happy to hang back and wait for their moments, however sparingly they come along.
And if Oli Burke had found his range after wriggling to the byline in the final action of the opening half, their tactic would have been completely vindicated.
As it was, Burke, with Abdoulaye Doucoure in attendance but unable to risk a challenge from behind, saw his lash across the box pushed clear by Jordan Pickford.
Everton’s opportunities were more frequent and exceptionally hard won.
In fact, to call Dominic Calvert-Lewin’s 29th-minute attempt an opportunity is a stretch.
If it qualifies as such, that is solely down to the ability of the player – which he demonstrated with a fabulous piece of chest control from Michael Keane’s raking pass.
Calvert-Lewin’s first touch befuddled Jack Robinson, who was staring at the Everton striker’s back as he sent his volley screaming past Aaron Ramsdale’s right post.
Ramsdale held on low to his left when Alex Iwobi tried his luck from 25 yards after receiving a pass from Gylfi Sigurdsson – the wind and greasy surface meant a punt from distance was always a fair option.
It was Iwobi – operating on the right, with Anthony Gordon making his first Premier League start this season on Everton’s left flank – who nearly undid Sheffield United with a mesmerising dribble.
Iwobi evaded four challenges to progress into the box but when Gordon took over the hosts had congregated behind the ball and the teenager ran into traffic.
Burke wasn’t alone in giving Everton a scare in the opening 45 minutes.
Ben Godfrey read play unfolding as Rhian Brewster slid a pass through for McGoldrick.
The forward had gone too soon and was offside but, as the ball arrived at his feet, nobody knew for sure.
McGoldrick went round Pickford and steered his strike on target, Godfrey sprinting back to swipe clear.
Then, in accordance with today’s instructions, the flag went up at the very last.
Everton had long periods pinning the home team in their own half.
Indeed, it was a source of frustration for Chris Wilder’s players that they couldn’t retain possession, often appearing hurried.
When McGoldrick tried to escape into attacking territory, he only succeeded in overrunning the ball.
Mason Holgate nipped in and was fouled, giving Sigurdsson his first chance – after 31 minutes – to whip in a dead ball.
Ramsdale got to it first. Then spilled it.
Godfrey struck the loose ball towards goal but had his strike blocked by Yerry Mina, who didn’t have time for evasive action.
Sigurdsson bent a 25 yarder past the right post five minutes before the break, Ramsadale a spectator, as he had been when a terrific early Iwobi cross scooted marginally out of Calvert-Lewin’s reach.
Oli McBurnie replaced Burke for the second half and the striker taking a tumble in the box with Keane at his back led to the most cursory of 57th-minute VAR reviews.
The contact was tenuous, Keane defending strongly to clear up after Mina’s initial interception on a left-wing cross.
Bernard replaced Gordon in a like-for-like swap two minutes earlier
Holgate couldn’t resist pulling the trigger when running onto a ball 25 yards out but was hight and wide with the strike.
The defender was almost immediately switched into the centre, with Seamus Coleman replacing Keane.
Godfrey chose the 71st minute to show off his fleet of foot.
Ethan Ampadu was left in Godfrey’s slipstream but Baldock was hot favourite to take the ball as the defender covered across.
Godfrey defied those odds and was upended but Ramsadale kept hold of Sigurdsson’s free-kick this time.
The ball wouldn't drop for Bernard after Calvert-Lewin steered Iwobi's hoisted ball back across goal, three defenders converging to deny the Brazilian.
But he wouldn't be denied soon after, Bernard's cushioned touch for Doucoure, allowing the Frenchman to tee up Sigurdsson's strike.
Ampadu's miscued cross was heading for the underside of Pickford's bar but the keep was alert and touched over.
Sheffield United launched all they had at Everton now.
Enda Stevens was furious with himself for shooting over from 10 yards and McBurnie glanced wide from a stoppage-time corner.
McBurnie skewed wide after Mina hooked another cross clear.
And moments later a number of home players sunk to their haunches despondent.
For Everton, it was high-fives all round, an acknowledgement of a professional job completed.
Value Of A Clean Sheet
One goal was all Everton needed to take three points from Bramall Lane.
The scoreless draw was looking favourite as we entered the final 10 minutes and a point would have been okay in the context of Everton's recent form.
But three Everton players combined in a moment of quality and quick-thinking to claim Everton's second single-goal win on this ground in five months.
Bernard could have still been rueing an opportunity missed after being crowded out when poised to shoot in the middle of the box.
But the South American stayed aware and maintained a good position.
He was on the end of the dropping ball after Chris Basham's clearance on Seamus Coleman's cross went more up then away.
Bernard's cushioned touch directed it to Abdoulaye Doucoure, who was alert to Gylfi Sigurdsson's run on his right.
The pass invited Sigurdsson to shoot and the Icelander accepted, burying the ball inside Aaron Ramsdale's right post.
It was a night when chances were very hard to come by but Everton's ability to concentrate and restrict their opponents ensured Sigurdsson's strike received maximum reward.
Everton have conceded only once in four Premier League matches, a marked improvement on a period when by common consent they were conceding too many goals.
There has been a switch in policy, with Everton's full-backs sitting deeper, while a four-man midfield, supplemented by Gylfi Sigurdsson, gives Carlo Ancelotti's side a solid look.
Dominic Calvert-Lewin's ability to take care of the ball is vital, enabling Everton to move up the pitch and remain a threat in attack.
Everton's resolve has been tested by some very good teams. Chelsea, Leicester City and Arsenal didn't muster a second-half shot on target between them.
Sheffield United went for an aerial bombardment after falling behind but, despite winning a handful of set-pieces, could find no way through.
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ANCELOTTI HAILS EVERTON'S 'MOTIVATION AND AMBITION'
No Away Day Blues
This victory was Everton’s fifth in eight Premier League matches away from Goodison Park this season.
Results outside L4 formerly represented an enduring ailment and one year on from Carlo Ancelotti’s first match in charge the signs point to Everton’s Italian manager finding a cure.
Ancelotti concedes empty opposition grounds level the playing field somewhat – and the same has been true at Goodison Park, where even 2,000 supporters have altered the complexion entirely.
But the point regarding Everton’s away form trending in the right direction holds nonetheless.
Winning three successive matches in London – against Tottenham Hotspur, Crystal Palace and Fulham – for example, creates a well of belief for future visits to the capital.
Everton had claimed three points only twice in 26 trips to London before opening this campaign with a controlled success at Spurs.
This encounter at Bramall Lane boasted all the ingredients for a slip up.
On a filthy night in South Yorkshire, Ancelotti’s side was confronted with a competitive and spirited home team, steadily regaining its feet after a terrible start to the season.
Everton were missing a clutch of integral performers and had only 72 hours’ rest after being winded by Wednesday’s late Carabao Cup quarter-final defeat.
Sheffield United last played six days ago, a relative luxury in this most relentless of seasons.
This was a night which takes it out of the legs, too, with the wind and rain sapping energy.
And the type of game which goes the other way if a team is unsure of itself.
Everton are increasingly comfortable in their own skin on enemy territory and remained composed and confident with this contest perched on a knife-edge.
When the chance came to win the match, they took it, then saw the reault over the line.
Ancelotti made immediate inroads in his bid to improve Everton’s football away from Goodison.
He won at Newcastle United two days after starting his Everton reign with a 1-0 home win over Burnley on Boxing Day late year.
There was a come-from-behind 3-2 triumph at Watford not long after and post-lockdown Everton won at the homes of Norwich City and Sheffield United.
It was notable that Everton began emerging from a poor run this season by winning against Fulham on the road.
Ancelotti’s side were close to three points at inhospitable Burnley but had to settle for one.
Then a trip to much-vaunted Leicester brought, perhaps, Everton’s most complete performance of 2020/21.
They were in charge from start to finish and the free-scoring hosts didn’t lay an attacking glove on Everton, failing to register a shot on target after half-time despite trying to recover a deficit.
Important Night For Duo
This wasn’t necessarily the sort of night kids harbouring professional football ambitions grow up dreaming about.
Playing in foul conditions on Boxing Day night wouldn’t have concerned Anthony Gordon and Tom Davies, however.
The two graduates of Everton’s Academy have been waiting for chances and they’d have snapped your hand off for this chance at a Bramall Lane stadium battered by unremitting rain and a swirling wind.
Gordon in particular has been waiting a while for this opportunity.
It was back on 12 July when he last started in the Premier League and before tonight his lone appearance from the beginning this season came in the Carabao Cup tie with Salford City on 16 September.
The 19-year-old has little opportunity to run at his opponents in the opening half.
Skilfully gathering a raking pass from Mason Holgate, though, Gordon showed intent to spin away from his marker, George Baldock, but couldn’t locate the final ball.
Gordon was tidy and disciplined. One effort to tack back and prevent David McGoldrick’s crossfield pass finding the overlapping Baldock drew an appreciative ovation from the dugout.
That episode was typical of the maturity in Gordon’s game. He keeps his position in Everton’s shape off the ball and more often than not makes the right decision in possession.
Gordon drew two men before rolling a pass to Gylfi Sigurdsson five minutes before half-time. Sigurdsson had the time and space to take aim and was fractionally wide.
Davies demonstrated his confidence moments later, trying a long pass over the top for Dominic Calvert-Lewin.
That ball was slightly overcooked but indicative of a combative and progressive display from the 22-year-old.
Davies had three Premier League starts this season prior to the game in South Yorkshire.
This was his third in the critical deep-lying position which his usually Allan’s domain.
Davies had huge boots to fill, then, and, as he did in victories over Brighton & Hove Albion and Arsenal proved a fine replacement for the Brazilian.
He never strayed too far forwards from his position in front of Everton’s defence, leaving the forward running to partner Abdoulaye Doucoure.,
Davies’ passing was fast assertive; there were a couple of accurate passes through narrow corridors for Sigurdsson and balls speedily fed wide.
On his 132nd Everton appearance, Davies drove through midfield with the ball and tried to spring his team on the attack.
Gordon’s night ended 10 minutes after half-time but it will have been a valuable outing for the promising attacker.
Davies went off on 74 minutes, hobbling slightly but having run himself into the ground.