The Gunners saw their title hopes ended by successive away defeats to Tottenham and then Wigan, but avoided another slip-up which could have allowed their arch rivals to steal the final automatic qualification place in next season's Champions League.
The Arsenal squad set off on a lap of appreciation after the final whistle of another season which promised so much, yet again failed to deliver a trophy as manager Arsene Wenger was left to reflect on just which summer transfer targets he can bring in to finally turn potential into silverware.
The Fulham fans, meanwhile, will be hoping their amazing European adventure brings a fairytale finish against Atletico Madrid in Hamburg on Wednesday night.
It was a low-key opening, before under-fire Arsenal keeper Lukasz Fabianski failed to collect a deep ball into the penalty area, which was hacked clear as Stefano Okaka looked to pounce.
Robin van Persie's five-month injury absence was seen as a major factor in Arsenal failing to last the distance.
The Dutchman's curling free-kick from the right had Mark Schwarzer backpedalling to tip the ball away.
Fabianski drew some ironic applause from the Gunners faithful after, at the second attempt, he held onto a deep free-kick into the Arsenal six-yard box.
It was, though, Schwarzer who would be embarrassed with an error on 21 minutes.
The Australian failed to control a backpass from Chris Baird, which gifted the ball to an alert Andrey Arshavin.
The Russian dashed to the goal-line, dribbled around the keeper and - with Van Persie screaming for a tap-in - promptly slotted the ball in off John Pantsil at the near post.
It was soon 2-0.
Theo Walcott - hoping to be in the England World Cup squad - beat the offside trap to latch onto Bacary Sagna's pass and dart into the right side of the penalty area.
He squared for van Persie, whose low drive cannoned off Schwarzer's legs and onto the bar, before the Dutchman blasted in the rebound.
Arsenal made sure of victory ahead of half-time when, on 37 minutes, Emmanuel Eboue flicked on Walcott's low cross into the six-yard box, which - with van Persie lurking - Baird stabbed into his own net.
Walcott should have made it four when played in by another clever backheel from Eboue, but dragged his angled shot wide from 12 yards.
At the other end, Okaka got ahead of Sol Campbell and into the Arsenal penalty box, but the ball would not fall for him as Fabianski cleared.
Fulham made a change at the start of the second half, as David Elm replaced Bjorn Helge Riise.
The Swedish striker almost had an instant impact as his low, 18-yard drive came back off the base of the post, but the offside flag was up.
Van Persie went close when Eboue's cross picked him out in the Fulham six-yard box.
Schwarzer redeemed himself with a smart reaction save, before the Arsenal striker then stabbed the rebound against the woodwork.
There was a worrying moment for Fulham when Pantsil - who had just recovered from a serious knee injury - needed treatment after pulling up when kicking the ball clear.
Fulham boss Roy Hodgson was taking no chances, and brought on Stephen Kelly after 56 minutes.
Arsenal also had to make a change when Swiss international Johan Djourou - who had not played all season because of his knee problem - replaced Mikael Silvestre, the veteran defender, out of contract this summer, possibly making his last appearance for Arsenal.
Fulham had a penalty claim waved away by referee Mike Jones when Campbell appeared to haul down Clint Dempsey as the ball was lofted into the Arsenal box.
The American took his protests too far, and was shown a yellow card, before he was replaced by Fredrik Stoor.
At the other end, Eboue was booked for diving after a sliding challenge from Kelly in the left corner of the box.
Fabianski darted out of his area to close down Elm, but handled and also went into the referee's notebook.
With six minutes left, substitute Carlos Vela made it 4-0 when he chipped Schwarzer after collecting Samir Nasri's throughball.