No side has beaten the Hammers more in the Premier League than their north London rivals, but Declan Rice’s 48th-minute finish was enough to hand Manuel Pellegrini’s men all three points.
It was difficult afternoon for Unai Emery’s side as they failed to find the back of the net for the first time in the league since the opening weekend of the season.
The visitors started the better, Alexandre Lacazette wasting the first good opening of the game after surging through the West Ham defence before shooting straight at Lukasz Fabianski, and then firing the rebound over.
The Hammers grew into the game, Samir Nasri missing a decent opening to net against his old club, failing to hit the target when played through on goal, while Sokratis did well to get in the way of Marko Arnautovic's strike on goal. The in-form Felipe Anderson then fizzed a low drive wide of the far post.
West Ham wasted their best chance of the half on the stroke of half-time when Rice flashed a header across the face of goal.
But the Hammers broke the deadlock three minutes after the restart when Nasri was given too much time in the box to roll the ball back for Rice, who smashed his first-time effort past Bernd Leno.
With Arsenal struggling to get back into the game, Pierre Emerick-Aubameyang wasted a glorious chance when firing over from close range. Alex Iwobi then went close with a shot across the face of goal.
The chances petered out for Arsenal as West Ham dug in to protect their lead, denying the Gunners the chance to go level on points with fourth-placed Chelsea.