Carlton Cole gave the Hammers the lead at the beginning of the second half, but Theo Walcott scored a quick-fire brace before Lukas Podolski secured the three points for the Gunners.
Despite dominating possession, Arsenal could not make the breakthrough in the opening period with only two of their 10 first-half shots on target.
They were made to pay for that profligacy as Cole struck within a minute of the restart. Wojciech Szczesny spilled Kevin Nolan's 20-yard strike, and the former England forward tapped home the rebound.
It was his fourth goal in his last four games on Boxing Day and gave the Hammers a surprise lead.
Sam Allardyce's struggling side had opportunities to double their advantage with first Szczesny denying Matt Jarvis, and then an unmarked Joey O'Brien sending a diving header wide.
Cole also had a great opportunity after Razvan Rat delivered a superb cross from the left but instead of stopping for the header, he opted for a side-foot volley which screwed wide.
Arsenal were on level terms after 68 minutes when Walcott's shot with his less-favoured left foot somehow found its way into the net.
The tame effort went through George McCartney's legs and Adrian, who was again preferred to Jussi Jaaskelainen, let the effort slip through his grasp.
Three minutes later, and Walcott had a second with an uncharacteristic thumping header at the back post after a fine cross from Podolski.
Adrian did smother a shot from the German substitute but could do nothing when Olivier Giroud, who has now only scored once in his last 13 games for club and country, held up the ball well and laid it back to Podolski, who nestled his effort in the corner.
The only sour note for Wenger was Aaron Ramsey going off in the 65th minute with an apparent thigh injury on his 23rd birthday.
A chorus of boos greeted the final whistle with Allardyce under fire and the Hammers just one point off the bottom of the Premier League table.
|West Ham vs. Arsenal: Player Grades|
|Joey O'Brien||C||Bacary Sagna||B|
|James Tomkins||C||Per Mertesacker||C|
|James Collins||C+||Thomas Vermaelen||C|
|George McCartney||C||Kieran Gibbs||B-|
|Joe Cole||C-||Mesut Özil||B-|
|Mohamed Diamé||C||Aaron Ramsey||B-|
|Mark Noble||B-||Theo Walcott||A-|
|Kevin Nolan||C||Mikel Arteta||B|
|Matthew Jarvis||C||Santi Cazorla||B+|
|Carlton Cole||B||Olivier Giroud||C|
|Razvan Rat||C||Lukas Podolski||B+|
|Guy Demel||C||Mathieu Flamini||C|
|Matthew Taylor||C||Nicklas Bendtner||C|
The frantic Christmas schedule continues as West Ham United entertain West Bromwich Albion in the Saturday lunchtime kick-off, while Arsenal have a little more rest before they visit Newcastle United on Sunday.