Arsene Wenger side Arsenal ended Manchester United's 25-game 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, Swiss playmaker Granit Xhaka opened the scoring with a deflected shot from distance, which looped over United goalkeeper David de Gea.
And they doubled their lead three minutes later when English striker Danny Welbeck headed home against his former club after a pinpoint cross from midfielder Alex Oxlade-Chamberlain.
Manager Jose Mourinho introduced striker Marcus Rashford and Jesse Lingard to try to rescue the match, but they failed to bring the Red Devils to life.
The result means The Gunners remain in sixth place but are two points off United in fifth and six points off Pep Gaurdiola’s Manchester City in fourth, with a match in hand over both teams.
Arsenal boss Arsene Wenger on a possible top-four finish: "We want to win our games. Some teams that are safe continue to fight. Let's focus to win our games. Every win is important. We had a bad patch and seem to have recovered from it."
On Welbeck's goal: "That's the kind of goal you want from Danny. He has all the abilities a striker needs. Hopefully, that will give him a boost."
Manchester United manager Jose Mourinho: "We made eight changes. Of course, we knew we were not coming in our maximum power. That's a decision. We want to try to win the Europa League - it's more important than finishing fourth.
"The last trophy I won was three months ago. I didn't care about that. Thursday is the match of the season. I hope Old Trafford feels the same, because we need Old Trafford."