The Dutchman admitted on Saturday morning that he sometimes exaggerates contact if he has been fouled, but produced a superb finish just after the break to give Arsene Wenger's side a win they barely deserved.
While van Persie produced the decisive moment of the contest, Wenger's side were indebted to stand-in goalkeeper Vito Mannone, who produced a series of fine saves to deny a spirited Fulham.
The Italian is only third-choice but time and again thwarted the hosts, who will slip into the bottom three if West Ham win at Manchester City on Monday night.
The 21-year-old was at his very best on 16 minutes when he produced a stunning double-save to deny first Andy Johnson, whose header was bound for the top corner, and then Clint Dempsey's follow-up.
Mannone actually saved the American's shot with his face, but Arsenal did not appear shaken from their stupor by this close escape and gave the ball all-too-regularly for Wenger's liking.
Mannone was again called upon to tip Zoltan Gera's effort round the post and after barely calling Fulham keeper Mark Schwarzer into action, the visitors would have been very relieved to have reached half-time with the game goalless.
And Arsenal made the most of that good fortune seven minutes after half-time when van Persie beautifully controlled Cesc Fabregas's through-ball and swept home.
Arsenal threatened on the break, with Nicklas Bendtner and Emmanuel Eboue both being denied by the ever-alert Schwarzer.
But eventually they were left to thank Mannone yet again as he saved from Bobby Zamora, Johnson and Dempsey as the visitors just about held on for all three points.