Alexandre Lacazette scored twice for the Gunners before Aaron Ramsey's brilliant finish and Pierre-Emerick Aubameyang's late double secured a third straight away win in the top flight – their best such run since October 2016.
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.
Unai Emery's side, who have won every game since back-to-back losses to Manchester City and Chelsea in August, are now third in the table, above rivals Tottenham on goal difference.
Maxime Le Marchand's timely interception denied Lacazette early on, but the France striker broke the deadlock against the run of play 29 minutes in, turning past Tim Ream and drilling home from six yards out, Nacho Monreal with the assist.
Fulham's back three looked exposed with every Arsenal attack and only fine work from Marcus Bettinelli stopped Alex Iwobi tapping home a second, but they snatched an equaliser a minute before half-time, Schurrle clipping a fine first-time finish over Leno after a good Luciano Vietto pass.
Bettinelli made an excellent one-handed save to deny Hector Bellerin just after the break, but he was beaten in the bottom-left corner barely a minute later as Lacazette blasted home his second of the game on the half-volley.
Any hope of another Fulham comeback was quelled with 23 minutes left, as Ramsey, 39 seconds after coming on, flicked a backheel in off the post after a super counter-attack gave Aubameyang room to cross.
Aubameyang sealed the victory in style, collecting Bellerin's cross and firing left-footed beyond Bettinelli on the turn, before striding onto Ramsey's pass and drilling into the bottom-left corner in injury time.
Lacazette looking lethal
Lacazette is flying under Emery this season and scored with his first two shots on target of the match at Craven Cottage.
Aside from his goalscoring, the forward's all-round play was a real highlight for the Gunners, who are reaping the rewards of the striker's increasing confidence.
