Fulham looked to be climbing out of the bottom three as they went 2-0 up early in the second half with two goals in three minutes from substitute Ashkan Dejagah and Fernando Amorebieta.
However, Hull produced a late comeback as goals from Nikica Jelavic and Shane Long earned the visitors a valuable point and denied Fulham a crucial three-point haul.
Fulham started the brighter of the two sides and John Arne Riise flashed a shot from the edge of the area well wide of the target after being teed up by Hugo Rodallega.
The home side really should have broken the deadlock on 12 minutes when Amorebieta fired over an inviting cross from the left which found Rodallega unmarked inside the six-yard box, but the striker failed to get contact on the ball to direct it goalwards.
Hull's Ahmed Elmohamady was booked on 18 minutes, much to the delight of the home fans, for diving as he tried to con referee Lee Mason when he went to ground wide on the right after going past Amorebieta.
Hull began to get a foothold in the game midway through the half, enjoying most of the possession, but they were struggling to test Fulham keeper David Stockdale.
The visitors felt they should have had a penalty five minutes before the break when Shane Long appeared to be pushed over inside the box, but Mason waved away the appeals of the Hull players.
Felix Magath made a double change at the break with Kieran Richardson and Dejagah came on for Lewis Holtby and Riise and they both had a major impact for the home side.
Whatever Magath said at half-time seemed to have the desired effect as Fulham showed more attacking intent in the second half and they were rewarded on 55 minutes with a fine strike from Dejagah.
Dejagh picked up a ball wide on the right and cut inside David Meyler before curling a superb shot into the top corner past stranded Hull keeper Steve Harper.
Fulham doubled their lead three minutes later when Amorebieta got ahead of Alex Bruce to brilliantly glance home Richardson's cross from the left to become the first Venezuelan to score in the Premier League.
Hull got themselves back into the game 15 minutes with a goal out of nothing as Sascha Riether, in sliding to cut out a pass, sliced the ball up into the air and against his own crossbar and Jelavic was on hand to head home the rebound from close range.
Hull almost grabbed an equaliser two minutes later when substitute Sone Aluko's deflected effort came back off the crossbar with Stockdale well beaten in the Fulham goal.
Fulham were happy to play on the break and the home side almost caught Hull on the counter attack ten minutes from time when Rodallega got down the left and crossed for Dejagah inside the six-yard box, but Harper did superbly to keep out his close-range effort.
Hull piled forward in search of an equaliser and they were inches away from scoring on 86 minutes when Stockdale brilliantly tipped Elmohamady's shot onto the post.
Fulham were hanging on and it was no surprise when Hull equalised three minutes from time when Aluko crossed for Long to head home past Stockdale.