Rasmus Hojlund's first Premier League goal secured a 3-2 win for Manchester United over Aston Villa after Alejandro Garnacho had scored a brace to claw their way back from two goals down in a breathless encounter on Tuesday.

Erik ten Hag's team, which had fans booing the players off the Old Trafford pitch at half-time, climbed to sixth in the standings on 31 points, while Villa, who lost for the first time in 11 games in all competitions, are third with 39.

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"Keep believing. I think our fans they deserved it. They are always behind us and we've had so many setbacks," Ten Hag said after the match. "So I'm really pleased from the performance of this team. What kind of team can handle and deal with the amount of setbacks we have had?"

After 1,027 minutes, Hojlund finally ended his league goal drought in the 82nd when a United corner bounced off John McGinn's knee and fell to the Dane. The 20-year-old swiped it in off the post and a few minutes later left the game to a standing ovation.

"It has been a while [waiting], but yes I am very happy. I am the happiest man alive right now," Hojlund told Amazon Prime. "You can see from the celebrations, as well. We believed in ourselves until the very end and got the win today."

McGinn scored for Villa in the 21st minute from a long free kick that sailed past several players and into the bottom left corner. Leander Dendoncker doubled their lead five minutes later from close range when an unmarked Clement Lenglet headed a corner kick back across goal.

United appeared headed for their ninth defeat in 19 league games before Garnacho netted his first in the 59th minute with a fierce shot from the centre of the box. He equalised for the hosts in the 71st after a give-and-go with Bruno Fernandes.

"It is a great feeling. We are Manchester United. We were two-nil down, but we never give up, and it was a great comeback from the team," Garnacho said.

United, who played for the first time since Jim Ratcliffe struck a deal on Christmas Eve to take a minority stake in the Premier League club, looked done and dusted at half-time, but their second-half transformation was remarkable.

David Brailsford, who is sporting director of Ratcliffe's Ineos Sport, sat in the directors' seats at the stadium and would have heard loud jeers after Dendoncker doubled Villa's lead, while the away fans sang "Old Trafford is falling down" and goaded Ten Hag with chants of "You're getting sacked in the morning."

The story of the match began to turn. Garnacho believed he had pulled one back for United minutes after the break when Marcus Rashford delivered a pinpoint pass and he calmly went around goalkeeper Emi Martinez and slotted home, but VAR showed he was offside.

United continued to attack in waves, with seven shots on target to Villa's four, and were rewarded in the final half hour.

Hojlund, who signed for United in August from Atalanta, had five goals in four Champions League games, but the striker's lack of league scoring had raised questions in recent weeks.

He answered them on Tuesday, and ten Hag, Garnacho and keeper Andre Onana took turns wrapping the young player in hugs after the final whistle.

"Yes I remember the goal," Hojlund said. "First-time finish in off the post, good finish so I am happy. I am happy for the three of us attackers as well because we showed a lot of character today, and a lot of confidence."