An evening full of late drama and controversy ended with Claudio Bravo cast as an unlikely hero and Pep Guardiola conducting a choir of Manchester City’s triumphant supporters as they chanted the Spaniard’s name in the wake of a penalty shootout victory that moved the Premier League leaders a step closer to their first trophy of the season.

Their passage to the semi-finals of the Carabao Cup was far from straightforward and there were times when Guardiola looked anything but happy with what he was seeing, in particular when it came to some of the highly contentious decisions made by the officials, but the smile on the City manager’s face at the end could not have been wider during those jubilant scenes at the end.

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Guardiola explained that his celebrations were down to the fact that he was so overjoyed to see a youthful and much-changed City team – only two players survived from the side that thumped Tottenham Hotspur 4-1 on Saturday – find a way to win a match that was torn from their grasp in the seventh minute of injury time.

Already annoyed that the fourth official had indicated there would be eight minutes of added time, Guardiola’s patience was stretched to breaking point when Bobby Madley, the referee, awarded a penalty after Demarai Gray tumbled to the ground following a challenge from Kyle Walker. Gray was clever in cutting across the defender but it was hard to escape the feeling that the Leicester winger made the most of any contact. Madley, however, pointed to the spot, Jamie Vardy converted and Guardiola’s players were staring at the prospect of playing an additional half an hour.

Facebook Twitter Pinterest Referee Bobby Madley points to the spot after Demarai Gray went down under Kyle Walker’s challenge. Photograph: Carl Recine/Action Images via Reuters

Walker ended up getting booked for diving later on and Ilkay Gündogan also received a yellow card for simulation. Guardiola was not interested in discussing any of those incidents in detail afterwards, including Leicester’s penalty, with the City manager preferring to praise his players for the character they showed to recover.

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Bravo was also singled out for praise after he saved Riyad Mahrez’s penalty in the shootout to give City victory. With Vardy clipping the outside of a post with Leicester’s previous penalty kick, Mahrez had to score but was denied as the Chile international flung himself to his left to beat the ball away. Bravo had also stolen the show in the previous round, when he made two saves in the penalty shootout victory over Wolves, although this was not the night to be getting carried away with his performance.

For much of the game it was hard to avoid the impression that he was a danger to his own team and at the same time easy to see why Ederson, who has taken over as City’s No1, is such an upgrade in goal. Bravo looked like an accident waiting to happen every time the ball was played back to him and on one occasion he was fortunate not to concede a farcical goal after Vardy put him under pressure.

With Phil Foden, Tosin Adarabioyo, Oleksandr Zinchenko and Brahim Díaz all starting for City, there was a youthfulness about Guardiola’s side, yet it was one of the more experienced players that fashioned their breakthrough in the 26th minute.

Gündogan picked the pocket of Kelechi Iheanacho, a former City team-mate, drove at the heart of the Leicester defence and chose the perfect moment to release Bernardo Silva with a clever pass. One on one with Ben Hamer, Silva showed composure as he slipped the ball through the goalkeeper’s legs to put City ahead.

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Claude Puel also rang the changes, leaving out seven of the players who started against Crystal Palace on Saturday, and it was not until the Leicester manager called for the cavalry in the second half that his team really started to cause City problems. Vardy, Mahrez and Gray all came off the bench and suddenly Guardiola’s players had a game on their hands.

The second half was stop-start as Ben Chilwell, Hamer and Eliaquim Mangala all required lengthy treatment, contributing to the eight minutes of injury-time that was added at the end of normal time. City still looked like they were going to see the game out but then Walker allowed Gray to get the wrong side of him, the winger fell to the floor and the referee gave a penalty that threw Leicester a lifeline.

Vardy swept the ball past Bravo but he was unable to repeat that feat in the shootout as City stretched their unbeaten domestic run to 27 matches.