Matt Jarvis silenced the Emirates Stadium by heading the visitors in front on 40 minutes, but goals from the German and Frenchman eased the pressure on Arsene Wenger
Matt Jarvis silenced the home crowd five minutes before half-time with a brave header from close range, but Podolski brought the Gunners level a minute before the break with a powerful low strike.
Giroud put Arsenal into the lead on 55 minutes when he expertly brought down a Thomas Vermaelen pass and fired through the legs of Adrian, and on 78 minutes Podolski lashed high into the net to seal a vital win.
|VIEW FROM EMIRATES STADIUM
|By Jay Jaffa
A number of home fans told a popular radio station in the build-up to this game that West Ham at home were Arsene Wenger’s bread and butter; the games Arsenal always won.
Well for a good portion of the first half they would have been glancing nervously around at the equally worried 50,000-odd home fans as Sam Allardyce’s side countered well and stole into a 1-0 lead via Matt Jarvis.
Trailing at home, it would have been easy to excuse this as a consequence of their 120 minutes at Wembley three days earlier but the Gunners know what’s required at this stage of the season better than any other club. The race for a top four spot is their domain and Lukas Podolski’s double sandwiched Olivier Giroud’s expertly taken goal as Arsenal rallied to claim all three points as they moved back above Everton.
With Hull, Newcastle, West Brom and Norwich to come, they may well have passed their biggest test. The pressure is on Everton.
The visitors, who remain seven points clear of the relegation zone, began the game with an urgency and pace as they pegged their hosts back in the opening 20 minutes.
Mohamed Diame had two chances to opening the scoring but saw his first effort blocked, and he skied a second over the crossbar from Andy Carroll's neat cut-back.
Arsenal finally burst into life 30 minutes in as Cazorla threaded a pass through to Giroud in the penalty area, but France international's half-hearted flick was easily saved by Adrian.
He was made to rue that finish as West Ham took the lead five minutes before the break.
Antonio Nocerino raced away from Kim Kallstrom, making his first Arsenal start, with Jarvis following in with a brave header after Wojciech Szczesny saved the Italian's shot.
West Ham's goal was the catalyst to set Arsenal into life and they were on level terms just four minutes later as Cazorla latched onto a poor clearance from Stewart Downing and found Podolski, who slotted home.
Ten minutes into the second half Giroud made up for his earlier miss to move Arsenal in front for the first time in the game.
Thomas Vermaelen delivered a lofted pass into the penalty area that the 27-year-old controlled superbly before firing first-time under Adrian.
Podolski and Cazorla both went close to extending the hosts' lead just after the hour, but Adrian saved well from the German and Cazorla's 20-yard strike was just wide of goal.
The points were sealed in the 78th minute as Podolski doubled his tally, the forward lashing his sixth league goal of the season high into the roof of the net after substitute Aaron Ramsey's headed pass.