Wenger's team climbed back above Everton into fourth place in the Premier League. The Gunners had fallen behind to Matthew Jarvis's first half header, but after Podolski equaliser Giroud produced a brilliant first touch and a lethal finish to put the hosts ahead.
Wenger admitted that his team desperately need a dominant period from Giroud in the race for a top-four finish.
"Giroud is a great guy with a great mentality,” said Wenger.
“He has gone through a difficult period which affected his confidence, but you could see he is refreshed now.
"It was a perfect first touch for his goal. You need that if you want to score. What I like is he used his upper body to make some space."
Meanwhile, leaving the likes of Aaron Ramsey and Alex Oxlade-Chamberlain on the bench, Wenger fielded his oldest starting eleven in the Premier League since May 2003.
"It was a gamble. I said before the game that it was one of the oldest teams I've ever played at Arsenal but I trusted their experience.”
Meanwhile, West Ham manager Sam Allardyce was vexed his side failed to press home their advantage, with Jarvis's decision to stay on his feet when fouled by Bacary Sagna in the penalty area another source of frustration.
"The facts are that referees don't give penalties when you stay on your feet,” said Allardyce.
“For honesty there is no reward.”
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