There have been few moments to match this level of fantasy from Manchester United in recent times. This is a club whose identity is built around turning impossible dreams into unforgettable realities but too many players have looked uncomfortable wearing that famous red shirt of late. The modern United have been too safe, too bland, and they have put out too many sides without the courage to deliver under pressure.

Not this time, though. This time there was magic. It materialised when Marcus Rashford, who turns 22 on Thursday, stood over a free-kick in the 73rd minute and decided to try his luck from 30 yards. Lesser players might not have had the confidence but Rashford trusted in his technique and produced something special, stunning Stamford Bridge with a rocket that wobbled through the air and flew into the top corner. “A bolt out of the blue,” Frank Lampard said. “No team can stop that.”

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Chelsea’s manager was right but Rashford’s individual brilliance was not the only reason United are through to the last eight of the Carabao Cup. This was also a strategic triumph for Ole Gunnar Solskjær, whose counterpunching tactics worked in the opening period, as did his decision to make two attacking substitutions when Chelsea were on top midway through the second half.

United, who are unbeaten in four matches, were rewarded for responding positively when Michy Batshuayi cancelled out Rashford’s early penalty with an excellent strike in the 61st minute. Instead of falling back, they rediscovered their attacking zest. Solskjær turned to his bench, bringing on Anthony Martial and Andreas Pereira for Victor Lindelöf and Jesse Lingard, and switching to a back four allowed United to regain control of a game that seemed to be slipping from their grasp.

“It shows the character of the team,” Solskjær said. “We were excellent, with fast football. That’s Manchester United. We’re trying to get back to that. Marcus has that strike in him. I’ve seen him in training so many times.”

Facebook Twitter Pinterest Willy Caballero launches himself full length towards the top corner but cannot stop Marcus Rashford’s dipping free-kick. Photograph: Robin Jones/Getty Images

While United celebrated, Chelsea absorbed the disappointment of their seven-match winning run coming to an end. There was a callow feel to a side containing four teenagers, a lack of oomph waiting to be exploited, and United were quick to put themselves about.

Fred had another good game in central midfield, Scott McTominay set the tone when he was booked for steaming into Mateo Kovacic early on and Lampard must have been alarmed when Harry Maguire won the ball off Marcos Alonso with a firm challenge before shrugging Christian Pulisic aside.

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United had disrupted Chelsea’s rhythm and were carrying the greater threat in attack. McTominay had gone close in the 13th minute, sweeping a shot just wide from Daniel James’s corner, and it summed up Chelsea’s unease when Alonso conceded the penalty that allowed the visitors to edge ahead midway through the first half.

A fine run from James, who was always available to receive the ball on the right, created the danger. The winger’s pace carried him deep into Chelsea’s territory and he was entitled to go down after being bumped from behind by Alonso. Chelsea’s left-back could have no complaints when Paul Tierney penalised him, though at least United’s recent struggles from the spot gave the Spaniard hope of a reprieve.

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Yet Rashford, who had seen a penalty saved against Norwich on Sunday, kept his nerve. He had also missed one against Crystal Palace in August but there was no doubt in his mind here, only the composure to send Willy Caballero the wrong way and plant the ball into the opposite corner.

Lampard was worried. He knew Chelsea’s passing had been slow. They did not manage a shot on target during the first half and Brandon Williams, United’s teenage wing-back, was coping well whenever Callum Hudson-Odoi ran at him on the right. Pulisic also found it hard to shake off Aaron Wan-Bissaka on the opposite flank.

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There were brighter signs from Chelsea at the start of the second half. Billy Gilmour, a slender 18-year-old, injected some urgency in midfield and Hudson-Odoi spurned two opportunities, scuffing wide after meeting Alonso’s low cross and firing over after latching on to a searching ball from Pulisic.

An equaliser was on the way and it arrived when Caballero punted a clearance towards Batshuayi. The striker had spent most of the match being bullied by Maguire but this time he made the United centre-back look clumsy and slow, nodding the ball away from him, turning sharply and charging towards the area. Maguire’s lack of pace had been exposed and Batshuayi fired beyond Sergio Romero from 25 yards.

Yet the last word went to United after Pedro, on as a late substitute, brought down Fred. Rashford stepped up and the best compliment that can be paid to him is that Cristiano Ronaldo would have been proud of what happened next.