Steve Sidwell had swept the hosts in front in the 26th minute, only for Robin van Persie to quickly equalise.
Bobby Zamora nodded the Cottagers back into the lead just before the hour with substitute Zoltan Gera shown a straight red card two minutes after coming on - but a late goal from Theo Walcott earned Arsenal a point as they finished fourth in the Premier League behind FA Cup winners Manchester City.
The Gunners had won just twice in their previous 10 league matches as a campaign which promised so much quickly fell apart after defeat in the Carling Cup final against Birmingham at Wembley.
Arsenal manager Arsene Wenger left the field to chants of "spend some money" from the travelling support, who will expect much better next time around.
Fulham saw most of the ball during the opening exchanges at a blustery Craven Cottage.
When Jack Wilshere - the centre of a club-versus-country row over his proposed inclusion in the Under-21s European Championship squad - did pick out Samir Nasri with a chip into the Fulham box in the 10th minute the Frenchman, just back from a hamstring injury, could only loop a tame header goalwards.
Arsenal's defence, so often their Achilles heel this season, played a very high line and were almost caught out when Andrew Johnson scampered clear, but was called back by a tight offside flag.
The visitors almost snatched the lead when Bacary Sagna whipped over a deep cross to the far post, where fellow full-back Kieran Gibbs' downward header was clawed away by Mark Schwarzer, who came close to joining the Gunners in the summer.
Fulham took the lead in the 26th minute when Arsenal defender Johan Djourou played Zamora onside as the England striker scampered away down the right before cutting the ball back to Sidwell, who drilled home from six yards.
The lead, though, did not last long.
Abou Diaby, so often an under-performer this season, won the ball in midfield, before playing a neat one-two with Marouane Chamakh to release Van Persie on the edge of the Fulham area.
The in-form Dutchman needed no second invitation, killing the pass with his first touch before dispatching a low strike into the bottom left corner to level on 29 minutes and take his tally to nine in consecutive away games.
Arsenal were, however, soon back on the defensive.
Thomas Vermaelen produced a brilliant goal-line tackle after Danny Murphy had barged into the six-yard box and stabbed the ball past Wojciech Szczesny.
At the start of the second half, Van Persie was booked for protesting after referee Martin Atkinson failed to award a foul when he was checked by Brede Hangeland.
Schwarzer denied Arsenal again with another fine save, this time turning Nasri's goalbound free-kick over the crossbar.
Fulham were back in the lead after 57 minutes when Jonathan Greening darted into the left side of the Arsenal box, before chipping the ball across goal where Zamora nodded in at the near post.
Szczesny was off his line quickly to deny Zamora the chance to poke home a third as Arsenal were on the back foot.
There was a let-off for Fulham, though, when Schwarzer spilled Van Persie's right-wing cross, but Chamakh could only stab the loose ball wide.
Arsenal made a triple substitution on 64 minutes, replacing Aaron Ramsey with Walcott, Diaby with Andrey Arshavin and Gibbs with Emmanuel Eboue.
With news filtering through of Manchester City taking a 2-0 lead at Bolton, Arsenal looked certain to finish fourth.
Arshavin almost released Wilshere with a neat pass, but the ball just ran away from the England youngster.
With 20 minutes left, Zamora, appearing to be carrying an injury, was replaced by Gera, who looks set to leave at the end of his contract this summer.
The Hungarian was soon walking off again however after his lunging two-foot challenge on Vermaelen was punished with a straight red card on 74 minutes.
With Fulham hoping to stay high in the Fair Play League table, and earn a chance at European football again in the summer, it could yet prove a costly dismissal.
Arshavin flashed a low drive just wide, before Walcott levelled in the final minute when his shot went in off the far post.