The Hammers opened the scoring through Jack Collison's fine strike in the 18th minute after he controlled on the edge of the area before firing through a crowd of players.
The second half saw a completely different Arsenal in action and threw down the gauntlet by scoring four times within ten minutes to put the contest beyond doubt prior to the hour-mark.
Olivier Giroud made it 2-1 in the 47th minute when he hammered home Theo Walcott's corner at the near post for his first goal since the end of December before Podolski teed up Santi Cazorla who produced a neat backheel.
A fourth goal was conjured when Podolski found space down the left before finding Walcott who fired home with a first-time effort before Giroud wrapped it up thanks to another Podolski pass.
The win has Arsenal still in sixth position but they are now just four points from fourth-placed Tottenham as West Ham stay 12th with a third loss in their past five.