Arsenal ended Manchester United’s 25-match unbeaten run in the Premier League and kept up their hopes of securing a place in the top four.
After a largely uneventful first half, Granit Xhaka opened the scoring with a deflected shot from distance, which looped over goalkeeper David de Gea.
And they doubled their lead three minutes later when Danny Welbeck headed home against his former club after a pinpoint cross from Alex Oxlade-Chamberlain.
Jose Mourinho introduced Marcus Rashford and Jesse Lingard to try to rescue the game, but they failed to bring the visitors to life.
The result means Arsenal remain in sixth place but are two points off United in fifth and six points off Manchester City in fourth, with a game in hand over both teams.
This victory not only reignites Arsenal’s chase for a Champions League place, but also ends an unwanted record for Arsenal manager Arsene Wenger against Jose Mourinho.
The pair have endured a fractious relationship over the years, and in their previous 15 competitive meetings Wenger had never beaten a Mourinho team, with his only victory coming in the Community Shield in 2015.
Sunday’s win ended the hoodoo and earned Arsenal only their 13th league win in 50 outings against the Red Devils.