The London club made up for their opening-day 3-1 defeat to Aston Villa, beating Martin Jol's side by the same scoreline at Craven Cottage.
A double from Lukas Podolski, to follow up an early goal from Olivier Giroud, saw Arsenal over the line despite a 77th-minute score from Darren Bent.
Arsenal also gave themselves a great chance of making the UEFA Champions League group stages with a 3-0 win away to Fenerbahce in midweek, but fans are keen to see heavy investments made in the squad before the end of the transfer window.
Yaya Sanogo remains the only addition to the ranks in the close-season, and with reports of a move for Real Madrid star Karim Benzema, Wenger has insisted their business is not yet done.
When asked whether the victory will alter his transfer plans, Wenger said: "No. We will be a bit less under media pressure maybe but that will not change exactly. I know exactly what I want to do and that will not change.
"Before next weekend? It's possible. Honestly, I'm not the only one that can decide that because the clubs who sell the players (are involved too).
"We are on the market, you know that. I know we expect news from us. We will try to give you some but at the moment, nothing to announce."
Wenger also confirmed that he yet to follow up an earlier bid for Newcastle midfielder Yohan Cabaye, which was rejected and described as "insulting" by Alan Pardew.
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