Matt Jarvis headed the Hammers in front at Emirates Stadium five minutes before half-time but Podolski equalised with a shot on the turn four minutes later.
It’s very important that we play next year in the Champions League. Today was the first step
Olivier Giroud’s classy touch and finish gave the Gunners the lead in the 55th minute, before Podolski powered home a second to wrap up victory 12 minutes from time.
The victory left Arsenal a point above fifth-placed Everton, who host Crystal Palace on Wednesday.
And Podolski told Sky Sports: “It was important that we switched onto the Premier League because we are fifth at the moment and we must fight for fourth place.
“It’s very important that we play next year in the Champions League. Today was the first step but now we must focus on the next game.
“The FA Cup final is after the season so we we’ll leave that for now and focus on the Premier League because the important thing is to play in the Champions League. The matches are absolutely amazing and it’s important for the club as well. Every player wants to play in the Champions League next year.
“You must understand that there are hard matches to come – we play away at Hull City and Norwich so it’s not easy. We must win all the matches and then I think we will qualify.”
Podolski also praised man-of-the-match Santi Cazorla, who set up the Germany international’s equaliser.
“Everyone knows Santi’s an amazing player and can give the final ball,” he added. “It was a pass between three or four players and not a lot of players in the Premier League can play a pass like this.”
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