Having missed a host of opportunities in the first half, Wenger's side fell behind to Carlton Cole's tap-in a minute after the interval, and then suffered a further blow when influential midfielder Aaron Ramsey was withdrawn in the 65th minute with a thigh injury.
Theo Walcott proved the catalyst for the turnaround, scoring twice in three minutes shortly afterwards, before Ramsey's replacement Lukas Podolski marked his first appearance since August with the third to seal Arsenal's fifth win in their last six visits to Upton Park.
After the game, Wenger praised the resilience of his side as they won for the first time in five games in all competitions.
"I'm proud of the character," he said.
"They are always focused and try to do well. We answered questions about our character today.
"People would have questioned us if we had not won today, or if we had lost.
"We have another good game against Newcastle (on Sunday) and that will be another test. The team wants to do well and he character is great.
"We had a difficult period but I think that was mainly down to the schedule, I think it was horrendous.
"When you do not win for four games it's important to come back for the confidence levels."
On Ramsey, Wenger confirmed that the midfielder had felt a problem in his left thigh and would be out of action for the immediate future.
"It looks serious, a thigh strain," he said.
"I don't know how serious but the Christmas period certainly is over. He knew straight away but we will have to see. I don't know how long, we will see tomorrow (Friday) morning."
