The only bright spot for Fulham on an otherwise dreary afternoon came when substitute Darren Bent scored a late consolation.
The Gunners bounced back from their opening day defeat at home to Aston Villa in some style.
Santi Cazorla and Theo Walcott pulled the strings in midfield as the visitors adapted better to the wet conditions, playing a counterattacking game that was designed to push forward at speed whenever Fulham lost
Both sides had chances in the horrid conditions but Arsenal made their efforts count and afterwards manager Arsene Wenger was ecstatic.
“We adapted our style of play. We were very dangerous at times, it was impressive, a good mix of patience game and speed game,” he said.
From the 14th minute when Giroud latched onto Aaron Ramsay’s mishit shot to dink the ball past David Stockdale the result was never in doubt.
Podolski settled matters with two great finishes either side of the break, the first a perfectly placed side foot from the edge of the area before squeezing the ball between two defenders to find the far post for his second.
The result led Wenger to express his hopes that it might take “some of the media pressure away.
“People always want news and we live in a world that is critical where everything is under scrutiny,” he added.
“I know what I want to do and one defeat since March will not change that.”