This is a night destined to remain etched in Everton history.
Not because Carlo Ancelotti's side eased through to an FA Cup fifth-round tie with either Wycombe Wanderers or Tottenham Hotspur.
No, for all the wizadry of James Rodriguez and a trio of good goals scored by Dominic Calvert-Lewin, Richarlison and Yerry Mina, this FA Cup tie will ultimately be recalled for Thierry Small becoming the Club's youngest player.
The left sider, with Everton since he was 11, came on for the closing five minutes and, at the age of 16 years and 176 days, pinched a record held by Jose Baxter since the forward played against Blackburn Rovers, aged 16 years and 191 days, in August 2008.
Tyler Onyango, a relative senior given he turns 18 in March, came on at the same time as Small for the midfielder's own Everton debut.
They both had their moments, too, Small depositing Kadeem Harris into touch with a muscular challenge and the tall Onyango pressing in midfield to drive Sheffield Wednesday's loan player from Chelsea, Izzy Brown, to distraction.
Everton's victory was set up by Calvert-Lewin, who converted an Andre Gomes cross after 29 minutes.
Richarlison's sixth goal of the season, heading home from a James Rodriguez corner after 59 minutes, doubled Everton's advantage.
And Yerry Mina completed the scoring from the same supply route three minutes later.
Everton were in control right from the beginning – disturbed only when Robin Olsen took off to his left to push behind a drive from Adam Reach after four minutes.
James was seeing an awful lot of the ball, a direct consequence perhaps of Everton’s control and movement.
Indeed, seconds before Calvert-Lewin forced the breakthrough, the Park End scoreboard flashed up in-game statistics which showed the home team operating with 74-per-cent possession.
There were spells when it appeared Everton had an extra man. Repeatedly, a blue shirt would pop up in space to receive a pass – the man on the ball having countless options.
One move on 17 minutes was of the highest order.
Abdoulaye Doucoure, Gomes and James were all involved, swapping machine-gun passes as Everton stealthily progressed infield from the right.
James eventually smuggled through a pass for Calvert-Lewin, who was denied by Joe Wildsmith at the foot of his left post.
Goalkeeper Wildsmith couldn’t keep out Calvert-Lewin for much longer, however.
Twelve further minutes elapsed before the England striker rejoined the goal trail with a strike that owed a lot to Calvert-Lewin’s anticipation and movement.
Gomes and Gylfi Sigurdsson combined to open up Wednesday on Everton’s left, Gomes injecting thrust by deceiving Joey Pelupessy to reach the byline.
The cross fizzed across the face of goal, reaching the back post where Calvert-Lewin got the jump on German defender Julian Bonner to slide in and score for the 15th time this season.
Wildsmith had touched a Richarlison header onto the bar after eight minutes, that opportunity created after James dropped deep for the umpteenth time in the opening stages.
The Colombian ultimately touched a gorgeous return pass for Seamus Coleman, whose deep cross invited Richarlison to head at goal.
Wildsmith got the faintest of touches to squeeze the ball over via the woodwork.
Richarlison was visibly miffed the ball didn’t go in and was similarly put out nine minutes later, despite defeating Wildsmith on this occasion.
The Brazilian got on the wrong side of Ciaran Brennan, one of three Sheffield Wednesday centre-backs, following James’ incisive through ball.
He finished unerringly but had begun his run too early and was a yard offside when James released the ball.
Sigurdsson smacked a shot wide after being teed by James – following more good work by the impressive Gomes on Everton’s right – as Everton tried to put the game to bed following Calvert-Lewin’s goal.
Perhaps stung by Rotherham United running them close despite falling behind in round three, Everton continued passing with intent and committing bodies forward.
On the rare occasions they went backwards, their manager asked, why?
James fed Coleman behind wing-back Ryan Galvin for a low cross that got stuck under Richarlison’s feet in front of goal.
Gomes sent a shot hurrying past the post as Everton pushed the away team after half-time - Ben Godfrey already heading wide after a James free-kick was helped across the box.
Wildsmith was equal to Calvert-Lewin’s angled blast but Wednesday were creaking.
A run of corners amounted to nothing – until one did, on 59 minutes.
James whipped it in from the right and Richarlison applied a glancing touch to send the ball inside Wildsmith’s left post.
Two minutes later and James repeated the trick, the only difference the identity of the player steering the ball into the far corner.
Meantime, Wildsmith saved brilliantly from Richarlison after a precise James pass.
When the corner was sent in, Mina climbed to put Everton out of sight.
Brennan got back onto his goalline to prevent a fourth after Calvert-Lewin strode onto another James pass to lift the ball over Wildsmith.
Holgate flung himself in the way of a goalbound drive from substitute Josh Windass to preserve Everton’s clean sheet.
And the home side’s position of comfort enabled Ancelotti to begin resting legs, Calvert-Lewin, Godfrey and Richarlison all granted time off, with Bernard, Anthony Gordon and Jonjoe Kenny – for the first time in five weeks – given a piece of the action.
Kenny was over with a presentable opportunity after Bernard’s initial effort was blocked by Osaze Urhoghide.
All that was left was for Small to become an Everton record breaker, joining the action alongside fellow debutant Onyango with five minutes remaining.
Dom’s Perfect Return
A boyhood Sheffield United fan, it could be tempting to conclude Dominic Calvert-Lewin has it in for the other team from the Steel City.
He scored both goals in Everton’s league cup win at Hillsborough last year and netted his third in two matches against Wednesday to put his team in front here.
The truth of it, however, is Calvert-Lewin has it in for everybody.
His strike to break the deadlock was a 15th this season for the 23-year-old.
Granted, it was his first one for a while – Calvert-Lewin was last on target when he bundled in an equaliser in Everton’s draw at Burnley on 5 December.
Even without his goals, Calvert-Lewin remained fundamental to Everton’s sequence of four wins from five Premier League games following the visit to Turf Moor.
His capacity to overpower defenders, protect the ball, run at speed beyond centre-halves and link-up play is integral to Everton’s football under Carlo Ancelotti.
There is no feeling to compete with that of scoring a goal for a centre-forward, however.
Refreshed following an enforced three-week lay-off, Calvert-Lewin swooped for the type of poacher’s finish that every top striker has in his locker.
He’d already had one effort saved by Joe Wildsmith when Andre Gomes and Gylfi Sigurdsson began speeding up an attack down Everton’s left.
When Gomes made to go past Joey Pelupessy, Calvert-Lewin started eyeing his options.
He went to the back post, ensuing any cross wouldn’t whizz past unmolested.
Calvert-Lewin could see the number on Julian Borner’s back and that spelt trouble for the defender.
Borner never really got a handle on Calvert-Lewin’s position and when Gomes’ delivery travelled to the back post it was turned in by the England striker.
Everton deserved the goal and there couldn’t have been a more popular scorer.
The hosts’ dominance enabled Anceolotti to give Calvert-Lewin a breather, the forward replaced on 67 minutes following a very pleasing return to action.
Holgate The Middle Man
Mason Holgate’s role in the middle of defence provided more evidence of the flexibility Carlo Ancelotti wants from his Everton players.
The 24-year-old counts centre-half as his favoured position but has been outstanding at right-back of late.
Operating to the left of Yerry Mina, Holgate confidently brought the ball forwards and defended soundly.
He stooped to intervene when Andre Green seemed poised to latch onto a ball heading for Everton’s box and was on the spot to hammer clear a menacing low delivery from Kadeem Harris.
Holgate was strong in the air – he didn’t lose a header all night – and quick across the ground, anticipating the direction of attacks to extinguish danger.
When Holgate met an Adam Reach cross with a cushioned pass on the volley, locating James Rodriguez on Everton’s right, it was typical of how the player took care of the ball.
He was unhurried and unfailingly chose to try to locate a teammate over simply clearing his lines.
There was a valuable headed interception to deny Calum Paterson a clear header at goal shortly after Dominic Calvert-Lewin’s 29th-minute goal.
In a competitive field, Holgate could lay fair claim to owning the loudest voice on the field, too.
He was constantly in the ears of Andre Gomes and Abdoulaye Doucoure in front of him – essentially providing the two midfielders with an extra pair of eyes – and noisily relayed instructions to Mina.
Holgate didn’t want to allow Sheffield Wednesday a sniff and when substitute Josh Windass directed a blast on target at 3-0, it was the Yorkshireman who threw his body in the way of the ball.
Elsewhere, James was returned to an assignment on Everton’s right and was imperious.
The South American created two goals with fine set-piece deliveries and repeatedly flummoxed Sheffield Wednesday with his vision and weight of pass.
A word, too, for Ben Godfrey. The Englishman played at left-back again and it is a measure of his consistency that we expect flawless performances in that position.
Godfrey was characteristically robust in the tackle and Wednesday had no joy whatsoever down his flank.
There were signs of growing confidence, too, in Godfrey’s intermittent bursts forward – most notably as Everton sought their opening goal.
Bright Beginning To Significant Week
Everton’s seventh win in nine matches represents the ideal start to a crucial week in a season full of them.
The priority here was to avoid Monday’s back pages and book a fifth round FA Cup tie in a fortnight.
Observing the bigger picture, Everton were returning from an unusually long break in this congested campaign and aiming to pick up where they left off at Wolverhampton Wanderers 12 days ago.
Rotherham United in round three provided a salutary lesson over the danger posed by Championship teams.
Equally, Sheffield Wednesday came to Goodison Park protecting a five-match unbeaten run – they won four of those games – and with relatively recent history on their side, Wednesday winning five and drawing three of their past nine trips to this ground.
Carlo Ancelotti’s team nevertheless did comprehensive justice to their favourites tag, sweeping aside their opponents to maintain the upbeat mood swirling around the Club ahead of Leicester City’s visit on Wednesday.
Leicester at home is among the Premier League’s most difficult fixtures.
Wins at Manchester City and Tottenham Hotspur are among seven victories from nine away matches this term for Brendan Rodgers’ team.
They sustained their own feelgood factor by coming through a tricky FA Cup tie at Brentford on Sunday.
The carrot for Everton in midweek is obvious: win and Ancelotti’s side will close within three points of third-placed Leicester, with two games in hand.
Either way, there will be scant time to reflect with Newcastle United due at Goodison on Saturday lunchtime.
It is the sort of schedule a team wants to tackle in high spirits.
By convincingly setting up an FA Cup meeting with either Wycombe Wanderers or Tottenham Hotspur, Everton ensured Leicester will be confronted by a home side feeling very good about themselves indeed.