Extra-time was needed - but Everton are into the third round of the Capital One Cup after producing a fine comeback to win a 5-3 thriller at Oakwell.
The Blues set up a trip to Reading next month by twice coming from behind to ultimately prevail against plucky League One Barnsley.
The hosts were two goals ahead at the break following strikes in quick succession from Sam Winnall and Marley Watkins.
But a sensational cameo from the bench by Gerard Deulofeu, who provided assists for three of the Toffees’ five goals, inspired Everton’s spirited fightback.
Kevin Mirallas and Steven Naismith struck to level the tie at the start of the second half before Dan Crowley put the Yorkshiremen back in front.
Romelu Lukaku forced the game into an addition half an hour, where an own goal from Marc Roberts put Everton ahead for the first time in tie.
Lukaku sealed the win with his second effort of the evening in the 116th minute, rounding off a crisp counter-attack.
Roberto Martinez made seven changes from the side that tackled Manchester City three days earlier. Matthew Pennington was handed his first-team debut, while there were maiden appearances of the campaign for Joel Robles, Muhamed Besic and Aiden McGeady.
Another player coming into the team was Bryan Oviedo, who fashioned Everton’s first opportunity of the game, cutting in from the left-flank and dragging his shot wide.
In goal for Barnsley was Adam Davies, a Toffees Academy graduate, and he did excellently to deny both Mirallas and McGeady with a fine double save on 10 minutes.
Everton had begun positively and Lukaku was narrowly off-target with a curling right-foot effort from outside the box that drifted just over the bar, as Martinez’s charges applied early pressure.
Against the run of play, Barnsley went ahead midway through the opening half. A loose ball in the box was not dealt with by the Blues defence and Winnall pounced to finish low into the corner past Robles, who’d had very little to do up until that point.
Everton searched for an immediate response and Mirallas, who went to ground under a dubious looking challenge inside the Tykes’ box, saw his appeals for a penalty waved away.
The home side hit Everton with a second goal on 28 minutes. A deep left-wing cross from Roberts found Josh Scowen at the far post and his header was scrambled over the line inside a packed six-yard area by Watkins.
Barnsley’s quick-fire double didn’t deflate the Toffees, who pressed and probed throughout the remainder of the first period for a route back into the tie.
Lukaku’s crisply-struck drive was charged down 10 yards out and Davies dived to his right to smother Tom Cleverley’s goal-bound curler. Besic also saw a venomous drive block before the half-time whistle.
Martinez freshened up Everton’s right side at the break by introducing Deulofeu and Ross Barkley for McGeady and Pennington, with Cleverley dropping down to full-back. The two substitutions proved pivotal as a dramatic second half unfolded.
Everton emerged after the restart with plenty of purpose and the deficit was halved by Mirallas almost instantly.
The ball fell kindly for the Belgian winger 12-yards out and he thundered a volley into the top corner of the net, much to the delight of the 4,200 Evertonians packed in behind Davies’ goal.
Substitute Barkley, who had already seen an earlier effort rise over the target, was just wide of the mark with a header as Everton pinned back the hosts with wave after wave of attack.
It was just a matter of time before the equaliser arrived - and it did on the hour mark through a thumping header from Naismith. Deulofeu created space down the right and his inch-perfect cross was nodded home by the Scotland forward.
The scores stayed level for less than a minute, however, as Crowley went straight up the other end to put Barnsley back in front. A cut-back from the right found the midfielder, who beat Robles with an angled low shot into the bottom corner from inside the D.
Back came Everton though and it took a brave challenge from Alfie Mawson under his own crossbar to prevent Lukaku from reaching the ball almost certainly converting from point-blank range.
There was then a strong shout for a Blues penalty when Oviedo appeared to be pushed to the floor inside the box, only for the appeals to waved away by referee Simon Hooper.
Deulofeu had illuminated the contest since entering the fray and after seeing his own claims for a spot-kick fall on deaf ears too, he provided another precise assist, this time for Lukaku to draw Everton back level again with just 10 minutes remaining.
The Club-record signing clinically converted, guiding his low finish under Davies to make it 3-3.
Late on, Everton were unrelenting in their search for a winner as Barkley, Naismith and Lukaku peppered the Barnsley goal, while captain Phil Jagielka and Mirallas had headers narrowly miss the target.
Despite the visitors’ best efforts, the tie went into extra-time - but it took the Blues only seven minutes of the additional period to conjure what proved to be the game’s decisive seventh goal.
Again Deulofeu was the creator, delivering a low centre from the right which unlucky Tykes defender Roberts bundled into his own net under pressure from Lukaku.
Barnsley, as they had showed all evening, had courage in spades and they were almost back in it when Conor Hourihane struck the crossbar with a dipping 25-yard shot in the second period of extra-time.
A pulsating tie was eventually secured for Everton when Lukaku collected Barkley’s slide-rule pass to finish off a counter-attack and book the Blues’ trip to the Madejski Stadium on the week commencing 21 September.