Lukas Podolski scored twice after Olivier Giroud had grabbed the opener for the visitors while Darren Bent tapped in a consolation goal on his debut for Fulham.
It is the second time in four days Arsenal have scored three goals, following Wednesday's 3-0 victory over Fenerbahce in their Champions League playoff.
Saturday's win and the manner of the performance will go some way to making up for their opening day slip-up at home to Aston Villa, while the names on the scoresheet might make fans think twice about demands for a new marquee striker.
"Yes, I'm pleased because we played like a real team. It is never easy to play away in the league and we did it convincingly," Arsenal manager Arsene Wenger told BT Sport.
Both teams have three points from their first two Premier League games after Fulham beat Sunderland in their first game of the season.
Despite their resounding midweek win, the pre-match talk still focused on Arsenal's need for reinforcements and the club's perceived failure to land a signing to excite frustrated fans.
"You can get people to focus too much on who you will buy and forget how good the players are here," Wenger added.
Giroud, who is often touted as one of the men Arsenal need to upgrade if they are to chisel out a title challenge, had his say in the debate with his third goal in as many games this season on nine minutes.
Aaron Ramsey tried his luck with a shot from distance that struck Giroud's heels and fell neatly into the Frenchman's path.
He lifted it delicately over keeper David Stockdale, standing in for the injured Maarten Stekelenburg, and into the net.
In atrocious conditions that made Arsenal's intricate passing game difficult, Fulham harried their north London opponents and should have been level but for a fantastic save from Wojciech Szczesny.
The Arsenal keeper parried a shot from Adel Taarabt but the rebound fell invitingly for Damien Duff charging in at the far post. His shot, however, was deflected away by Szczesny's feet as he scurried back into position.
It was a let-off for the visitors, who went on to double their advantage four minutes before the break.
Santi Cazorla sent Theo Walcott free down the right, his shot from the angle was pushed out by Stockdale, but Podolski followed up and blasted his effort into the net from the edge of the area.
The German made sure of the points midway through the second half when he latched on to Cazorla's cross and fired in from the edge of the area for his second of the match.
Bent came off the bench on 58 minutes for his first appearance following his loan move from Aston Villa and grabbed a typical poacher's goal, tapping in at the far post with 13 minutes to play.
(Reporting by Toby Davis; editing by Pritha Sarkar and Stephen Wood)
