Pierre-Emerick Aubameyang scored both goals for the Gunners, one on either side of halftime. Chelsea's American star Christian Pulisic scored but left the game due to injury.
Pulisic scored just five minutes in to give the Blues early control, but Aubameyang scored a penalty kick in the first half and then put home a brilliant winner in the 67th minute that was a bit controversial due to a possible foul in the build-up.
Chelsea finished the game with 10 men following Mateo Kovacic's questionable red card in the second half, earning his second yellow for a challenge on Granit Xhaka.
The result is a massive one for the Gunners, who finish the season with a trophy, qualify for Europe and get revenge on their fellow London club after losing the Europa League final to them last season.