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Arsenal, finding a spark and much-needed self belief after successive league defeats by title-chasing Manchester City and Chelsea, ran riot with four goals in 12 mad minutes after the break having fallen behind in the first half to Jack Collison's goal.
Podolski, recalled after illness, quickly levelled with a superb strike from 25 metres. Giroud's volley made it 2-1 soon after the restart before German international Podolski, causing mayhem on the left flank, set up Santi Cazorla, Theo Walcott and Giroud to leave shellshocked West Ham 5-1 down before the hour.
West Ham were forced to play with 10 men for the final 18 minutes after substitute Daniel Potts was carried off on a stretcher with a serious-looking leg injury following lengthy treatment on the pitch.
Arsenal stay sixth but are now one point behind Everton and four behind fourth-placed Tottenham Hotspur after 23 games.
West Ham, with one league win in their last eight, remain 12th.