Arsenal got off to a dream start when Eddie Nketiah netted twice within the opening 10 minutes, before Leeds went down to 10 men when captain Luke Ayling was shown a straight red following a VAR check just before the 30 minute mark.
But despite Mikel Arteta's side dominating the entire match, Leeds pulled one back in the second half through Diego Llorente.
The result helps Arsenal keep a hold on the final Champions League spot, four points ahead of north London rivals Tottenham Hotspur, while Leeds slip into the relegation zone after Everton beat Leicester 2-1.
Arsenal came firing out of the blocks and struck early, with Nketiah capitalising on Illan Meslier failing to control a backpass to nip in and turn the ball into the empty net after five minutes.
Nketiah, who spent some time on loan at Leeds in 2019-2020, doubled Arsenal's lead on 10 minutes, diverting a Gabriel Martinelli cross into the goal to become the first Arsenal player to score twice within the opening 10 minutes of a Premier League game for 20 years.
Things went from bad to worse for Leeds when Ayling was shown a straight red card for a reckless two-footed challenge on Martinelli after a VAR check upgraded the yellow originally shown by referee Chris Kavanagh.
Arsenal were unlucky not to get a third just before the break, when Martin Odegaard fired a free kick from outside the box towards Meslier. The goalkeeper got a hand to it on the line, leaving defender Llorente to clear under pressure.
The hosts continued to push for another but it was Leeds who struck first after half time when Llorente volleyed the ball past Aaron Ramsdale on 66 minutes from their first corner of the match.
Leeds gained momentum from the goal, and gave everything they had, with Jesse Marsch sending Meslier up into the Arsenal area twice to try and find the equaliser, but the hosts held onto their lead to seal all three points.