Bobby Zamora had headed Fulham into the lead in the first half, but after having two goals disallowed, Blackpool grabbed two goals in quick succession late in the second half.
Debutant Luke Varney played a crucial part in each, his shot producing an own goal from John Pantsil for the first before he swept home a clinical finish from Brett Ormerod's through pass 14 minutes from time.
However, Dickson Etuhu scored with three minutes remaining from a classy move by Fulham to ensure the points were shared.
Mark Schwarzer was again absent for Fulham as he awaits his prospective move to Arsenal to reach a conclusion, so David Stockdale continued in goal for the visitors. Another absentee was Paul Konchesky, the left-back on the brink of a move to Liverpool.
For the home side, Varney made his debut after signing on a season-long loan from Derby, while Ormerod started up front with Marlon Harewood missing through injury.
A raucous atmosphere swept round a sun-kissed Bloomfield Road and Eliott Grandin dragged a shot wide from 25 yards after five minutes.
Blackpool were dominating the early stages and had the ball in the net on 17 minutes. Ormerod was the man to turn it home with his head, but he had done so from an offside position.
At the other end, Fulham threatened through Clint Dempsey but Ian Evatt made a fine last-ditch tackle, exactly a week on from a similar challenge leading to him being sent off in the 6-0 defeat by Arsenal at the Emirates.
Varney was afforded his first sight of goal in a Blackpool shirt midway through the first half, latching on to a pass down the left channel and firing a shot narrowly wide of the far post with Stockdale beaten. Fulham then also had a ‘goal’ disallowed, as Blackpool goalkeeper Matt Gilks had been bundled into the net by
The tight pitch at Bloomfield Road was much more to Blackpool’s liking than the expanses of the Emirates the previous week, as they hassled and harried their opponents to good effect.
Yet on 35 minutes, Fulham took the lead. Damien Duff fed Moussa Dembele on the right flank and the new signing’s pinpoint cross picked out Zamora to head home from close range. It was arguable that Zamora was offside when the cross was played, but the goal stood and Fulham had the lead despite being second best through the opening stages.
Charlie Adam took it upon himself to try and get Blackpool back into the game. First from a free-kick near the touchline, he tried an audacious shot that looped over Stockdale but onto the roof of the net, fooling the home crowd that it had gone in instead of over the bar. Soon after, Adam fired in a shot from 25 yards with his weaker right foot but it swerved wide of the post.
Duff was causing problems with his quick footwork, and he had a sight of goal three minutes from half-time with a cleverly worked corner, but pulled his shot wide of the near post.
The second half began in much the same manner as the first, with Blackpool forcing most of the play, and Evatt forced a save out of Stockdale when he struck in a shot as the ball bounced around in the Fulham area.
Goalscorer Zamora had the first effort on goal in the second half at the other end, a flick-on from Dempsey inviting him to try his luck with a volley, but Cathcart managed to make the chance difficult enough that the Fulham striker's shot could not trouble Gilks.
As the hour mark passed, Fulham were looking more and more comfortable on their lead, with Blackpool resorting to long balls.
It was from one such punt forward that the game's most controversial incident came. Stockdale was challenged by Varney under a high ball, and as the two players fell to the ground, Grandin was on hand to smash into an empty net. However, the referee's whistle had gone for a foul on Stockdale, much to Ian Holloway's displeasure on the sideline.
Ormerod had a header drift wide of the post before Blackpool got the goal their play so richly deserved. Varney found space on the right of the box and although his shot was deflected away from goal by a defender, Fulham's Pantsil clumsily sliced it into his own goal to send Bloomfield Road into raptures.
Blackpool rode that wave of support to press for a winner, and within two minutes of the goal, Adam's clever left-foot shot had to be clawed over the bar by Stockdale.
It wasn't completely one-way traffic, as Dempsey's swerving shot from distance forced a fine save from Gilks low to his left.
But Blackpool were to take the lead with the next attack, Ormerod rolling a perfectly weighted pass into the path of debutant Varney, who smacked a low shot beyond Stockdale. As if Pantsil's afternoon had not been bad enough, it was his poor positioning that played Varney on in the build-up to the goal.
However, Fulham were not to be denied. Dembele collected the ball in midfield and played a magnificent pass into the path of Etuhu, whose run had not been tracked. The Fulham man kept his composure to lift the ball over Gilks and into the net for the equalizer.
There was still time for Simon Davies to draw an excellent flying save from Gilks deep in injury time, but the points were to be shared.
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