A 3-1 opening day loss at home to Aston Villa resulted in Arsenal supporters questioning Arsene Wenger's status as manager, expressing their unhappiness at the Gunners' lack of progress in the transfer market.
A 3-1 victory in the Champions League qualifying first leg at Fenerbahce quietened the dissenters and first-half strikes from Olivier Giroud and Podolski lifted the mood further.
Germany striker Podolski, who has been linked with a move away from London as Wenger bids to reshape his squad before the September 2 closure of the transfer window, converted another devastating Arsenal counter-attack for a third.
On-loan Aston Villa striker Darren Bent netted on his first Fulham appearance in reply.
Bent has now scored for six clubs in the top flight, but that was as good as it got for the Cottagers, playing in front of new owner Shahid Khan.
Arsenal made two changes from the side which started the win in Istanbul.
Carl Jenkinson replaced Laurent Koscielny, with Bacary Sagna moving to centre-back, and Podolski was brought in for Jack Wilshere, who was on the bench.
Former Tottenham midfielder Scott Parker made his debut for Fulham, who beat Sunderland last weekend, to play for his fifth London club.
Arsenal had the better of the opening skirmishes in torrential rain.
Source: PA
Source: PA