Substitute Lewis McGugan slotted home a late winner for the visitors, who defended desperately to withstand some even later Hull pressure to cement their place in the play-off positions.
George Boyd had given the home side the lead on the stroke of half-time, but Darius Henderson equalised shortly after the restart.
The hosts took just 90 seconds to produce their first effort on goal, with Robbie Brady's powerful 30-yard free-kick ruffling the side-netting and fooling half the ground into thinking it was in.
The hosts' first clear chance fell to Boyd after 15 minutes, although the on-loan Peterborough forward knew little about it when Robert Koren's free-kick was parried into his path by Karl Darlow, the Scot poking the ball over from six yards.
Hull twice missed out on taking the lead midway through the first half. Jack Hobbs saw his header from Gedo's cross tipped over before the Egyptian latched on to Brady's excellent centre moments later only to nod the ball straight at Darlow.
The Tigers went ahead in first-half stoppage time when Hobbs headed Koren's corner back into the danger zone and, as the ball bobbled around, Boyd produced a clever finish with his back to goal, flicking the ball over his shoulder and the stranded Darlow.
Hull might have doubled their advantage five minutes after the break when Gedo beat a dallying Danny Collins to a long ball upfield and centred for Boyd, whose effort was blocked by the recovering Welshman.
Forest responded immediately, Simon Cox's powerful effort from the right channel deflecting narrowly over before a slice of good fortune allowed them to equalise in the 54th minute.
Radoslaw Majewski's cross from the left found Cox six yards out and the former West Brom man volleyed against the bar, but the ball rebounded kindly for Henderson, who made no mistake from 12 yards.
Neither side had any intention of settling for a point. Cox was a whisker away from putting the away side in front when he narrowly failed to get a crucial touch on Collins' header back across goal from Chris Cohen's 67th-minute free-kick, while at the other end Stephen Quinn had his low effort well saved by Darlow.
There were just five minutes remaining when Collins' long ball was knocked down by Dexter Blackstock to fellow substitute Billy Sharp, and his drilled effort across the box fell to McGugan, who rolled the ball home from eight yards.
Enterprising wing-back Brady had already seen three free-kicks whistle inches past the frame of the goal, and his 88th-minute set-piece was even closer as it rebounded off the inside of the post before falling to substitute Jay Simpson, whose shot was scrambled off the line by Cohen.
Hull were again denied by some last ditch defending when, deep into injury time, David Meyler's header was hacked out from under his own crossbar by Henri Lansbury.
Steve Bruce's men still did not give up, but their fate was sealed when Gedo fired over from six yards after Darlow parried Boyd's speculative effort.