The Gunners had slumped to successive defeats against Manchester City and Chelsea to leave them facing an uphill battle to regain a place in the top four. Wenger knew there was no more margin for error, but must have feared another night of frustration after falling behind in the rearranged Boxing Day fixture to a fine strike from Jack Collison.
However, Lukas Podolski crashed in a 25-yard effort to equalise before the break. Olivier Giroud then netted twice while Santi Cazorla and Theo Walcott also got on the scoresheet as Arsenal romped home. "We got a good response," said Wenger.
West Ham had to play the closing stages with 10 men after what looked a serious injury to substitute Daniel Potts, who was carried off on a stretcher following a serious head injury and kept in hospital overnight for observation.
Wenger added: "I could not predict that we would score five goals, but what was vital for us was to equalise before half-time and then see if West Ham could maintain their control of us.
"In the second half from the start on we created chance after chance and played at a very high pace. From there on it was great movement, great quality in our final balls and in our combination play. Until Potts got injured of course, after that it was the end of the game because we played 11 against 10 and it was [already] 5-1."
West Ham's evening was overshadowed by Potts' injury, with the player set to spend the night under observation after momentarily being knocked unconscious.
Irons boss Sam Allardyce admitted the start to the second half had been "a horrible 12 minutes for us".
He added: "When you concede as early [in the second half] as we did and they get into top gear, you have to give their players credit for their top spell. You wonder what Arsenal are going to be like when they have lost two on the trot, once we opened up they tore us apart.
"My strategy was working brilliantly until half time, I had planned to introduce fresh legs and talent. But by the time I blocked it up, they were 5 ahead. It was the worst 45 minutes I've suffered this season."
Source: PA
Source: PA