Victor Adeboyejo put the Reds ahead but the visitors levelled on the stroke of half-time then took the lead in the second half. That started a mad ten minute spell in which Jordan Williams equalised then Liam Lindsay made it 3-2 before Cauley Woodrow won and missed a penalty.
The visitors then levelled to force a shoot-out in which they scored all five of their spot-kicks while Mamadou Thiam saw his saved by impressive City stopper Thomas Scott.
Daniel Stendel picked a strong side despite making six changes from the side who won 4-2 at Southend United in the second round of the FA Cup on Saturday.
He played Victor Adeboyejo, Jared Bird and Williams – youngsters but with some senior experience – while the rest of the side were first team regulars including in-form striker Cauley Woodrow.
Barnsley had the first chance of the match as Lindsay headed over Dani Pinillos’ right-wing corner in the fourth minute. City could have gone ahead when Jeremy Frimpong’s low right-wing cross was turned just wide by Taylor Richards from close range.
The home side took the lead in the 17th minute when Williams swapped passes with Woodrow and sent in a perfect low cross from the right which Adeboyejo fired past the goalkeeper from eight yards out. It was the 20-year-old striker’s fourth of the season but his first in exactly three months.
Woodrow thought he had made it 2-0 by tapping home Brad Potts’ right-wing cross but it was ruled out by the linesman for offside. Woodrow then latched onto a Mike Bahre pass and went through on goal but the ball ran away from him and was cleared by a defender.
City almost levelled when James Bolton fired over six yards out on the turn after Ethan Pinnock had only half-cleared a right-wing cross from Ian Poveda.
Potts – who earlier blazed over an ambitious volley from the right of the box – missed an easier opportunity when a deflected Thiam shot fell to him and he fired high ten yards out.
Thiam then found Bahre with a clever pass but the German shot straight at goalkeeper Thomas Scott from the edge of the box after beating a man. Scott made a much better save, getting down to his left to brilliantly deny Woodrow who volleyed from 15 yards out after Adeboyejo had run down the right wing and lofted up a cross.
But Barnsley paid for those missed chances when Rabbi Matondo skipped through the centre of their defence and, after Davies saved his initial effort, he tapped into the open net with virtually the last kick of the half.
Ten minutes after the break, Adeboyejo headed a Dani Pinillos corner wide, but it was the visitors who went 2-1 up. Poveda fired into the bottom right corner from the edge of the box following a good individual run.
The lead lasted only a minute as Williams brought down a left-wing cross by Bahre in the box and fired in for his first career goal. Stendel then brought on Mowatt whose corner from the right was glanced in by the head of Lindsay.
It was almost four goals in ten minutes when Woodrow saw a penalty saved by Scott diving to his right after the same player was fouled in the box when City lost the ball to Adeboyejo.
It was 3-3 on 74 minutes when Barnsley were cut open by a counter-attack which was led by Matondo and finished when Poveda ran onto a through ball and beat Davies one-on-one.
Woodrow almost put the Reds back in front when goalkeeper Scott miskicked a clear to the edge of the box and, after Potts nudged it him, the Barnsley striker’s 15-yard shot was too close to Scott who parried it away.
Top-scorer Kieffer Moore was brought on for the final two minutes of added time but it was his fellow replacement Mowatt who nearly won it with a vicious 20-yard volley which went just wide of the bottom right corner.
Moore and Mowatt both scored their penalties, as did the other substitute Jacob Brown, but Thiam saw his clawed out of the bottom right corner by Scott.
Barnsley team (4-4-2): Davies; J Williams, Pinnock, Lindsay, Pinillos; Bahre (Mowatt 60mins), Potts, Bird (Moore 89), Thiam; Adeboyejo, Woodrow (Brown 82). Subs: Greatorex, McGeehan, Moncur, B Williams. Goals: Adeboyejo 17, Williams 60, Lindsay 65. Yellow cards: Lindsay.
Manchester City (4-3-3): Scott; Frimpong, Sandler, Garcia, Ogbeta; Pozo, Bernabe (Nmecha 66), Richards; Poveda, Bolton, Matondo. Subs: Dionkou, Rosler, Moulden, Gomes, Dele-Bashiru, Garre. Goals: Matondo 45, Poveda 59, 74. …
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