The humblers of Manchester United were easily second best in a match that towards the end seemed like a casual training session for Arsene Wenger's men.
Arsenal took the lead within 100 seconds following some clinical finishing by Eduardo. Cesc Fabregas picked up possession on the right flank and delivered an early cross into the area.
Then, in one smooth movement the Croatian striker cushioned the ball on his chest before letting it drop onto his left foot to volley the ball across goal into the right side of the net beyond the dive of Robert Green.
West Ham seemed to compose themselves quickly and on six minutes Mark Noble saw his chipped effort bounce just wide of the right post.
A Carlton Cole effort on 12 minutes following a defensive error from Justin Hoyte, was deflected just wide of Manuel Almunia's left post. The resultant corner delivered by Noble was deflected towards his own goal by an Arsenal player, but the ball was cleared off the line by Gael Clichy at the near post.
Two former Arsenal players then went close within seconds of each other five minutes later. First Fredrik Ljungberg capitalised on an error by Emmanuel Eboue and had a good shot saved at the near post by Almunia.
Then Matthew Upson found the ball at his feet from the corner that followed, but skied his shot when a goal looked more likely.
Within seconds however the Gunners had doubled their lead. Almunia rolled the ball to Clichy whose long pass upfield was nodded forward beyond his markers by Adebayor who, from the acutest of angles, redirected the ball into the net off the right upright.
West Ham were certainly try every which way to get back into the game and John Paintsil turned to acrobatics with an athletic overhead kick that had Almunia scampering as he watched the ball eventually bounce just past his left post.
The Gunners should have gone further ahead had Adebayor spotted his strike partner on 42 minutes. The Togolese attacker sped head down towards goal, failing to glance to his right where Eduardo was in space in front of goal, and with his finishing ability, a goal looked certain.
A minute later the Gunners had a penalty claim waived away as Jonathan Spector looked to have handled and went in at half time with the momentum and favourites to secure all the points.
Eduardo came close to adding to his and Arsenal's tally on 59 minutes when he was on the end of a cross just two yards out, but, under good pressure from Upson, he directed his effort just wide.
That was his last contribution as he was replaced three minutes later by Theo Walcott. The substitution saw a switch in tactics with Adebayor being asked to play a lone role, with Walcott being part of a three behind him supported by Flamini and Fabregas operating in more withdrawn positions.
Arsenal looked to be happy with a 2-0 win and West Ham's work had started to become ragged. Dean Ashton was brought on to relieve the hard-working Cole, but the result was a less mobile West Ham.
Adebayor and Tomas Rosicky came close to scoring in the 80th minute. The former's clever floated shot sailed just wide of the right post and the Czech midfielder was thwarted by the alertness of Green, who came out well to smother a shot from inside the area.
From then on the home side just kept possession to claim all the points to finish the day as they began the New Year, top of the Premier League.