Arsenal are now third on the Premier League, following their 2-0 win over Newcastle on Monday night.
The Gunners came into the game in sixth place, knowing that if they avoid defeat, they will overtake both Manchester United and Tottenham Hotspur.
Aaron Ramsey, who was captain for the day, opened scoring in the first half, as Unai Emery's men seized control of the fixture at the Emirates.
However, Arsenal had to wait until the second half to seal victory, through Alexandre Lacazette's delicate lob.
The victory took them up to 63 points, two more than United and Spurs.