For a long time it looked like bottom team West Ham would be able to hold on.
In the 79th minute, the home team's Mateus Fernandes created the best scoring chance of the match, but Arsenal's David Raya made one of the most important saves of his career.
Four minutes later, Martin Ødegaard passed to Leandro Trossard, whose shot broke the deadlock.
"An incredible feeling. I don't know what to say, I'm just very happy. I'm very emotional, but we have two important games left," said Norwegian Ødegaard on Viaplay's broadcast.
West Ham then thought they had equalised from a corner, but the goal was ruled out after VAR intervened, ruling that Raya had been fouled.
The Gunners now lead the league by five points over second-placed Manchester City, who have a game in hand. West Ham remain in the relegation zone with just two games left to play.
Swedish Viktor Gyökeres played the entire match for Arsenal.
