Manchester United were exposed in embarrassing fashion before the interval, then somehow rallied to give themselves a lifeline via a courageous second-half display. Manchester City remain firm favourites to reach the Carabao Cup final after the second leg in three weeks but Pep Guardiola’s side really should have killed the tie here. For Ole Gunnar Solskjær there is relief this did not finish as a hiding that could have seriously damaged his young side.

The remarkable element of how City came close to destroying United is that it is only a month since the tables were turned at the Etihad Stadium when United gave the champions a lesson in the 2-1 Premier League win.

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This, though, particularly before half-time, was more emphatic from City. If they score early in the return leg the rout they threatened here could materialise on their own ground.

Solskjær had started Mason Greenwood at centre-forward and made Marcus Rashford captain of his boyhood side for a first time. Guardiola started with Gabriel Jesus and Sergio Agüero on the bench, the manager deploying Bernardo Silva as a quasi-focal point in what would prove a masterstroke in the dominant first-half display. The atmosphere crackled and so did United, briefly, via a breathtaking move that featured Fred dancing round Ilkay Gündogan and ended with Rashford gliding into City’s area and pinging in a ball the holders scrambled clear.

Indeed, for the opening 10 minutes or so United were impressive. Jesse Lingard, Andreas Pereira, Daniel James, Greenwood and Rashford were a unit City struggled to catch as Nicolás Otamendi committed a series of fouls. Then Silva intervened. After the visitors at last took hold of the ball, Kevin De Bruyne rolled it to Kyle Walker. He roved forward and fed the Portuguese who fired a 25-yard finish into David de Gea’s top-right corner that gave the goalkeeper no chance.

Facebook Twitter Pinterest Brandon Williams fell to the floor rather, allowing Manchester City to score. Photograph: Robbie Jay Barratt - AMA/Getty Images

City’s supporters were jubilant and United were stunned. It allowed Guardiola’s team to relax with Silva chief tormentor.

Guardiola was unhappy with Otamendi’s and Benjamin Mendy’s reluctance to play quick balls along the latter’s left flank but he was about to be delighted with the second goal.

It began with a loose Victor Lindelöf header that went straight to Silva. He punished his opponents with a pinpoint pass into Riyad Mahrez, who slipped in behind the defence, skated round De Gea, and slid the ball into the unguarded net.

City’s third had a hint of farce about it. Silva – again – unlocked the door, hitting a pass from halfway into the path of Mahrez. He found De Bruyne and, when Brandon Williams intervened, the young left-back ended in a heap on the turf. Solskjær believed a foul was committed but the Belgian was allowed to continue forward. His shot was saved by De Gea only for the ball to ricochet off Pereira and in.

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United had to reach the break “only” 3-0 down as this was threatening to be a humiliation. City were rampant: Sterling fluffed a chance to add another – one of a few spurned openings – and when Mike Dean blew for half-time his whistle was accompanied by boos from the home support.

Solskjær’s response was to take off Lingard – who was feeling the effect of a recent virus – for Nemanja Matic to try and even up the midfield numbers in the second half.

The sense though, was that United would surely secretly have been happy with the match ending 3-0. They were still something close to shell-shocked, a condition Guardiola was intent his team should exploit further.

The manager was unhappy whenever they did not look forward, as when Walker and Mahrez engaged in keep-ball near him. Each time City attacked they looked menacing, so Guardiola’s stance was understandable. Mahrez had taken over from Silva as City’s conductor-in-chief and his dazzling feet first won a corner, then had him driving a shot at De Gea. To United’s credit they continued playing. Williams is only 19 but his willingness to dribble forward and ignite a move as the hour mark neared was admirable. This did not mask the underlying issue, though: City were in cruise control and could again expose United at any moment. After Rashford blasted a free-kick over, Solskjær took James off for Angel Gomes but hoping a 19-year-old would help salvage something was optimistic.

It was Rashford who did so. De Bruyne found Rodri but he was pickpocketed by Greenwood. The forward passed to the No 10 and after he slid beyond Claudio Bravo the tie was suddenly alive again.

It was barely credible yet near the end Bravo had to save another Rashford effort and United, remarkably, had been the better since the break.