Marcus Rashford scored a hat-trick after coming on as a second-half substitute, as the Red Devils turned on the style to dismantle their highly-rated German opponents.
Mason Greenwood gave Manchester United the lead midway through the first half with a super finish after being played through by Paul Pogba.
Rashford's first was set up by Bruno Fernandes, before Fred set up his second after winning the ball high up the pitch.
Anthony Martial scored a penalty, and then set up Rashford's third goal on the night, to cap off a perfect performance from Ole Gunnar Solskaer's team. Here is how each player fared for Manchester United.
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Manchester United Player Ratings
David de Gea - 6/10
He made a superb stop to keep out Konate's header from close range. A clean sheet will do his increasing confidence even more good.
Aaron Wan-Bissaka - 8/10
The right-back had another sensational performance. Angelino was mostly Leipzig's out-ball, as they looked to him to creat chances. The Brazilian could not live with Wan-Bissaka's tackling ability.
Victor Lindelof - 7/10
He was dominant in the duel against Yussuf Poulsen. There was also a certain swagger about the way Lindelof passed the ball out of the back tonight.
Harry Maguire - 7/10
The Manchester United captain was outstanding in defending balls into the box. His aerial prowess couldn't be matched by any of the RB Leipzig attackers.
Luke Shaw - 6/10
He defended well enough against Henrichs and Nkunku, and got forward when he had the opportunity to. He played in a superb cross in the second half, that Martial should have scored off.
Nemanja Matic - 5/10
He was a bit slow to get to the play in the first half, and allowed Leipzig to easily pass the ball around him at times. He was replaced by Scott McTominay in the second half.
Fred - 8/10
The Brazilian was superb in midfield for Manchester United. His energy set the tone for their performance, and was infectious as his team-mates fed off him. He nicked the ball off Marcel Sabitzer to set up Rashford's second goal of the game.
Paul Pogba - 7/10
Starting on the left side of the Manchester United midfield diamond, Pogba had an influential game. He helped the Red Devils unlock RB Leipzig in the first half with a lovely pass to Greenwood.
Donny van de Beek - 6/10
In his first start for Manchester United, van de Beek was a little subdued, but showed glimpses of why the Red Devils have brought him to the club. His awareness in tight spaces and movement were terrific in this game. He'll get even better when he settles in to the side.
Mason Greenwood - 7/10
He's such an instinctive finisher, and that was evident again tonight, as he placed a lovely finish into the far corner past Gulacsi. He will hope that this performance can be the start of him beginning to put away the off-field trouble that has marred him in the last few weeks.
Anthony Martial - 7/10
In the end, he finished with a goal and an assist, but that might not have been indicative of his performance as a whole. He was guilty of overplaying in the box, when the better option might have been to take a shot instead.
Scott McTominay - 6/10
He replaced Matic and continued to do what he does best, as he broke up Leipzig attacks well at the base of midfield.
Marcus Rashford - 10/10
Talk about impact substitutions! Rashford was outstanding tonight, as he kept threatening the RB Leipzig defence, with his runs in behind. His goals were outstandingly well taken. He would also have potentially given Dayot Upamecano plenty of sleepless nights with that performance.
Bruno Fernandes - 7/10
His peach of a thorugh-ball set up Rashford's first goal, and gave Manchester United breathing space in the game.
Edinson Cavani - N/A
He came on late in the game for his second Manchester United appearance.
Axel Tuanzebe - N/A
Came on alongside Cavani, and helped see out Manchester United's clean sheet.
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