Even signing a contract worth millions may not have been the highlight of Kobbie Mainoo’s week. The poster boy for the Michael Carrick revolution at Manchester United capped the transformation in both his fortunes and theirs with a goal whose significance was as much emotional as financial.

United clinched their return to the European elite. “Qualifying for the Champions League felt off in the distance at one point,” said Carrick. He has made it a reality. And though a draw was all his side required, the winner Mainoo drilled in completed a double over Liverpool, ensured a comeback from Arne Slot’s side that was simultaneously inspired and illogical was in vain, and gave United further reasons to appoint Carrick. “I love doing what I am doing,” he said. “It feels pretty natural.”

He looks a natural fit. He has been on quite a run. He has beaten Manchester City, Arsenal, Chelsea and now Liverpool. “We have beaten some very, very good teams,” Carrick said. He can feel the manager for the big occasion. Mainoo can save his goals for them. He has only struck eight times for United, but they include a winner in a Manchester derby that doubled up as an FA Cup final and now a decider against Liverpool. For a Mancunian and a United fan, each has come with a resonance. “I used to dream of times like these,” he said.

He has gone from marginalised to magnificent, aided by Carrick’s backing. “You want to follow him and fight for him and die for him on the pitch,” said Mainoo. With each game, it renders it still more ridiculous that Ruben Amorim did not rate him. Amorim, and his misguided tenure, can look more and more of an aberration.

Even on a day when United’s thoughts turned to Sir Alex Ferguson, who was taken to hospital after feeling ill, this was a game to offer echoes of his reign, full-blooded entertainment with plenty of attacking. Ferguson, you sense, would have enjoyed this. “Hopefully the result gives him a good boost,” said Carrick. To cite one of Ferguson’s more famous quotes, Liverpool may not have been knocked off their perch by United this season but they have lost twice to them. It is a simple explanation of why they are separated by six points.

Liverpool still need four to be sure of their place in next season’s Champions League. In a performance of two halves, they offered contradictory conclusions. They were shambolic at the start, mounted a comeback seemingly out of nothing and yet suffered an 18th defeat of the season. When their supporters chorused “champions” after half an hour, they had rarely looked less like them. Yet a depleted group showed a spirit.

They exposed some vulnerabilities in Carrick’s team; and yet, as has often been the case of late, United camouflaged them with victory. It was, remarkably, a third 3-2 win of his brief reign. It was greeted rapturously.

This is a club that has regained its self-confidence. Old Trafford was rocking. A buoyant side made a fast start, perhaps fittingly given the crowd included Usain Bolt.

They were two up inside a quarter of an hour. Whereas Liverpool lost Mohamed Salah and Alexander Isak to injury, United welcomed back a forward, in Matheus Cunha. Another with a flair for the major stage, the Brazilian had already scored against Arsenal and Chelsea. Now for Liverpool.

He struck at the second attempt, after his first shot was blocked by Ryan Gravenberch, bobbling in a shot from the edge of the box. The third-choice goalkeeper Freddie Woodman, continuing to deputise for the injured Alisson, was soon beaten again.

“United deserved to be 2-0 up,” said Slot. “They have a lot of strengths but two are definitely the set piece and the counter-attack and we fell in that trap. Then everything we have done before deserves a lot of criticism.”

Slot felt the second should have been ruled out but first found fault with his side. Woodman parried Bruno Fernandes’ header on to Benjamin Sesko’s thigh and it went in. Replays suggested it flicked his fingers but the Slovenian survived a VAR check. “If it was a touch, it should have been disallowed,” said Slot. “But the second goal we didn't concede because of a handball, we conceded it because we lost the ball in a stupid position and we lost a few big moments afterwards in duels. We have to first look at ourselves.”

But since Amorim’s January sacking, no one has more Premier League goals than Sesko. Yet the game turned in part when the Slovenian went off at half-time with a shin problem. His replacement, Amad Diallo, was only on for 90 seconds before he misplaced a pass, Dominik Szoboszlai ran 50 yards and slotted a shot past Senne Lammens.

It was an illustration why Szoboszlai is Liverpool’s player of the year; at times, this has been a one-man, valiant effort to transform games and a season. He was the inspiration for a fightback, first with a goal then an assist. Yet Lammens contributed, too, with an awful pass to Alexis Mac Allister. He found Szoboszlai who gave Cody Gakpo a tap in. Stuck on 49 Liverpool goals for 12 games, he brought up his half-century.

United’s superiority had been almost embarrassing in the first half. They risked losing in the second. In a redemptive moment, Lammens hooked the ball off his line after Virgil van Dijk met Szoboszlai’s free kick. Liverpool threatened to go from ragged to rampant.

But they offered little control either. “If you are 2-2 coming back from 2-0 down you should at least come out with a draw,” Slot said. “Two setbacks could have knocked us,” said Carrick, but United responded. And while Szoboszlai was catalytic for Liverpool, Fernandes was similarly influential for United. Perhaps the difference was that he had more of a supporting cast. And when Mac Allister miscued a clearance, Mainoo drilled in a shot from the edge of the box. “A great finish for them,” rued Slot. And it is shaping up as a fine end to the season for United, Mainoo and Carrick, too.