It only took nine minutes for Viktor Gyokeres to put the Gunners ahead.
Tomas Soucek pulled one back for West Ham in the 49th minute when he guided home Malick Diouf’s pass from close range.
Antoine Semenyo opened the scoring for the hosts in the 24th minute.
Arsenal fans will now focus their attention on the game between Liverpool and second-placed Manchester City on Sunday.
City controlled 67 per cent of the ball and registered 14 shots, yet could not breach a resolute Sunderland defence on a freezing New Year’s Day in the North East.
Daniel Ballard doubled the lead with a stunning strike before French international Wilson Isdoe sealed the victory, curling a superb effort into the far corner.
However, playoff spots to determine the remaining one team to join already promoted teams are guaranteed for both Luton and fourth-placed Middlesborough.
