Carlton Cole scored his fourth successive Boxing Day goal to give the Hammers the lead 48 seconds after the restart, before Walcott scored a quick-fire brace.
Podolski put the gloss on the result on 79 minutes as the Gunners went back to the summit.
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Mohamed Diame warmed the hands of Wojciech Szczesny on 25 minutes when he fizzed a left-footed effort from 25 yards straight down the throat of the Poland keeper.
Theo Walcott spurned a golden chance minutes later when he side-footed wide after escaping round the back of the West Ham defence.
Santi Cazorla came close with a dipping shot just after the half hour mark, but the shot could not come down in time before it flashed over the bar.
Moments later, Olivier Giroud was sent scampering through but the French striker sent the effort wide with his left foot.
Mikel Arteta struck a low effort narrowly wide from around 25 yards after Cazorla's freekick had bounced to him off the West Ham wall.
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Cole converted the opener when Szczesny spilled Kevin Nolan's side-footed effort straight into the path of the Hammers striker.
However, Walcott restored parity when he crept inside and hit a left-footed effort that squirmed through Adrian in the West Ham goal on 68 minutes.
The England international gave his side the lead when he met a cross with a thunderous header two minutes later.
German international Podolski made the result safe 11 minutes from time after he rifled in a low effort from the edge of the box after Giroud showed good strength to tee his teammate up.