The Frenchman fielded a team with an average age of 29 at the Emirates, with Olivier Giroud their youngest outfield player at 27, as he banked on his golden oldies to get a result.
Wenger, renowned for developing young players, opted for a wealth of experience to overcome stubborn West Ham and wrestle back fourth place, and the last Champions League qualification spot, from Everton who are a point behind with a game in hand.
"It was a gamble," Wenger told a news conference. "I said before the game it was the oldest team that I have ever played at Arsenal since I've been here."
In fact he fielded an Arsenal team with an average age of 30 against Leeds United in 2003 but his point was valid.
"I trusted the experience of the players," said Wenger. "Tonight it was an unusual around 30 (years of age) team and that experience helps when your backs are against the wall."
Arsenal reached the FA Cup final on Saturday on penalties against second-tier holders Wigan Athletic but, without a win in four league games and with the semi-final having taken its toll, Wenger decided older heads were needed against West Ham.
Goals from Lukas Podolski either side of a sublime Olivier Giroud finish secured the win for Arsenal, who fell behind to a Matt Jarvis header five minutes before halftime.
It was Giroud's strike, his 14th league goal this season, that especially pleased Wenger, who hailed the France striker's mental toughness after a tame finish in the first half when played through on goal caused uproar amongst the home fans.
"Olivier is a great guy with a great mentality," Wenger said. "At halftime he came in and was very down because he missed a great chance but he responded well in the second because mentally he is a strong guy."
Giroud, who was dropped from the starting lineup against Wigan, held off the challenge of two defenders to deftly bring down Thomas Vermaelen's long ball and strike his shot between West Ham's goalkeeper Adrian's legs.
"It was a perfect first touch," the Arsenal manager said. "What I like is that he used his upper body first to make some space and despite that he managed to have a great first touch, and he finished well.
"He's come through a difficult period. I think it affected his game for a while and his confidence. Tonight you could see that he was refreshed and up for it."
Arsenal now have 67 points and four games left, one ahead of Everton who host Crystal Palace on Wednesday, and they will be confident they can hold off the challenge of their rivals who have more difficult fixtures in their remaining five games.
"We know we have to win our games and hope Everton slip up somewhere," Wenger told reporters. "Lets focus on our job. At the moment we can only do it (finish fourth) if we win all of our games, so let's focus on that."