The German produced two classy strikes either side of the break to add to Olivier Giroud’s opener as Arsene Wenger’s side picked up their first points of the new Premier League campaign.
It was the perfect end to a difficult week for the Gunners, who have recovered from their opening-day defeat by Aston Villa to record successive victories on the road.
After their 3-0 win at Fenerbahce in Wednesday’s Champions League play-off first leg, England midfielder Jack Wilshere was surprisingly named as a substitute by Wenger, with Tomas Rosicky drafted into a three-man midfield alongside Aaron Ramsey and Santi Cazorla.
Fulham manager Martin Jol handed debuts to new signing Scott Parker after he completed his move from Tottenham Hotspur earlier in the week.
Adel Taarabt was also given a chance to impress on the left flank, but Darren Bent had to settle for a place on the bench following his loan switch from Aston Villa.
It has been a summer of change at Craven Cottage and new owner Shahid Khan was introduced to the home supporters before kick-off amid soggy conditions by the River Thames.
The Pakistan-born businessman was given a rapturous welcome as Fulham looked to build on last weekend’s opening victory over Sunderland.
A deluge of rain as the game kicked off made for a frenetic start and it was Arsenal who settled first, with an effort from Podolski being deflected wide for a corner.
More pressure in the 14th minute saw John Arne Riise make a last-ditch clearance with his head, but Arsenal kept possession and worked the ball to Ramsey. His shot from distance lacked power, but it struck Giroud on the heel and fell perfectly for the Frenchman to finish coolly.
Fulham’s response was almost instant as Taarabt forced Wojciech Szczesny into a smart save and the goalkeeper also did well to deny Damien Duff at the second attempt.
Left-back Sascha Riether almost created a chance to equalise seven minutes before the break, but Mertesacker’s outstretched left foot denied Fulham.
From the break, Walcott set up Kieran Gibbs but the defender could not follow his goal in Turkey on Wednesday as he dragged wide.
Once again, though, that was only a warning of what was to come as another quick break saw Stockdale save well from Walcott and the ball fell for Podolski to hammer into the unguarded net four minutes before the interval.
Fulham had reason to feel hard done-by and they began the second half with real purpose, with Taarabt forcing Szczesny into a smart save at his near post.
Ramsey almost put the game beyond Fulham when his effort was deflected wide and with the game running away from the hosts, Jol threw on Bent alongside Dimitar Berbatov.
However, it was not long before his side found themselves 3-0 down as Podolski rounded off a flowing move by picking his spot from Cazorla’s pass.
Bent did manage to pull one back with 13 minutes to play after he tapped home a cross-shot from Berbatov, but by then it was too late.