Story of the match
Nuno Tavares opened the scoring for Mikel Arteta's side, before Bukayo Saka converted from the penalty spot for the second time in two games.
Cristiano Ronaldo got one back for the Red Devils, but a second half thunderbolt from Granit Xhaka secured the win and all three points for Arsenal.
The Gunners took an early lead through left back Tavares, who was quickest to react when David De Gea made a save from Saka's curled effort, prodding home from close range.
Eddie Nketiah had a goal ruled out for a tight offside by VAR just before the half hour mark, but a penalty was consequently awarded for a foul in the build up, which was converted by Saka, his second goal in two games.
United got a goal back minutes later through their main man Ronaldo, who put the ball in the back of the net from close range to score his 100th Premier League goal.
Ralf Rangnick's side were awarded a penalty 10 minutes into the second half, after goal scorer Tavares handled the ball from a corner, but Portuguese midfielder Fernandes could only hit the post to squander a huge chance to equalise.
Five minutes later, Ronaldo had the ball in the back of the net for a second time in the game, but VAR ruled the goal out for offside.
The Red Devils were really starting to pile to pressure onto the Gunners, with Diogo Dalot being brilliantly denied by keeper Ramsdale, who was able to tip the ball onto the post.
Against the run of the play Arsenal restored their two goal cushion through Xhaka, with the Swiss midfielder firing a trademark shot into the back of the net from long range.