The Frenchman took his tally against Arsenal's London rivals to five goals in his last five Premier League games before playing a part in late strikes for Aaron Ramsey and Mathieu Flamini.
West Ham battled valiantly despite being under the cosh for much of the first half, before Giroud justified his inclusion ahead of Monday’s FA Cup hero Danny Welbeck when he finished off a well-worked move shortly before the interval.
Theo Walcott, meanwhile, was one five Arsenal changes from that cup win over Manchester United, and he should have opened the scoring following Giroud's neat backheel early on.
The hosts' early onslaught continued, as Sanchez's header was saved by Adrian before Kevin Nolan had West Ham's first effort on target - volleying at David Ospina following positive play down the left from Matt Jarvis.
That sparked a good spell for Allardyce's side, although Ramsey - another to come into Wenger’s XI - almost beat Adrian with an improvised effort off his knee as Arsenal started to regain the upper hand.
After several wasted Arsenal chances, Giroud finally rewarded his side’s persistence in first-half stoppage time when he capped off wonderful interplay with a fierce left-footed strike.
The Frenchman then clipped the ball in for Cazorla this time to find substitute Flamini for a close-range finish six minutes from time, ensuring Arsenal's 10th consecutive home win in domestic competition.
