Andre Schurrle had brought Fulham level at half-time, but it is now five defeats in eight games for Slavisa Jokanovic's side, who have conceded 21 times in those matches this season.
Aaron Ramsey, Alexander Lacazette and Emerick Aubameyang scored for Arsenal while Ander Schurrle got the only goal for Fulham.
The fact that the player has not dipped in form and has continued to do his best in the Unai Emery's team still makes him a light in the eyes of clubs who will want to have him.
Fulham are searching for their second win since promotion from the Championship.
Aubameyang whipped over a low cross that was slightly behind Ramsey, prompting a superb adjustment from the Wales midfielder as he guided a back-flicked shot into the far corner. But they showed the quality, the pace, the strength too'.
Aaron Ramsey scored a contender for goal of the season within a minute of taking to the pitch after missing out on the trip to Azerbaijan in midweek. The Gabon striker wasn't finished yet and, in the last minute, he smashed in Ramsey's pass for his sixth goal of the season.
Emery urged his players to continue improving after nine wins on the bounce in all competitions.
- Arsenal have a 51.5% win rate in Premier League London derbies (124/241) - the best in the division.
Aubameyang completed the rout with a long-range drive in stoppage time.
After the global break, Arsenal resume their Premier League campaign at come against Leicester City on October 22, before a Champions League clash away at Sporting Lisbon and a London derby with Crystal Palace.
Fulham's next outing is on October 20, when they travel to struggling Cardiff City in a game that looks even more important after both sides' losses this weekend.