Hull had been in the driving seat in Tuesday night's Championship clash after hitting back through Sone Aluko and Stephen Quinn following Matt Phillips' early goal for Blackpool.
But visiting boss Ian Holloway made two inspired changes by bringing on Kevin Phillips and Dicko, and after veteran Phillips levelled after 70 minutes, Dicko produced a piece of magic to claim the spoils for the Tangerines.
Hull defender Paul McShane was handed his first start of the season in place of the injured James Chester in what was the only change for the Tigers.
Gary Taylor-Fletcher gave Blackpool a boost by recovering from a back injury and he was just one of six alterations to the side that lost at Cardiff, with Barry Ferguson, Tiago Gomes, Neal Eardley, Nathan Delfouneso and Isaiah Osbourne also returning.
After a cagey opening 10 minutes, Blackpool broke the deadlock with their first attack of the game as an unmarked Matt Phillips fired Delfouneso's cross past the dive of Ben Amos from 10 yards.
Jay Simpson blazed wildly over for the Tigers, before Alex Bruce produced a terrific last-ditch tackle to deny Delfouneso as he bore down on goal.
A mistake from Ian Evatt presented a chance to Simpson, but his effort was saved by Matt Gilks.
The Tigers were piling on the pressure and there were big shouts for a penalty as Aluko went to ground under a challenge from Stephen Crainey, but referee Scott Mathieson only awarded a corner.
From the resulting set-piece, the ball into the box appeared to strike Tiago Gomes' arm, but again the appeals fell on deaf ears.
Six minutes before the break, Hull were level. Aluko received the ball midway inside Blackpool's half and looked around for support before letting fly with a brilliant effort from 25 yards that found the back of the net.
As the rain lashed down, a terrific ball from Aluko put Simpson in the clear, but he stumbled, lost control and the chance was gone.
Hull took the lead inside two minutes of the second-half through Quinn. A great ball from Aluko found the Irishman near the byline and from an acute angle he dispatched a clinical shot into the far corner.
Ahmed Elmohamady shot straight at Gilks, a Quinn effort was deflected for a corner by Osbourne, and then Abdoulaye Faye headed over as Hull pressed for a third.
Despite all City's pressure, Blackpool equalised after 70 minutes. Crainey swung over a free-kick, Taylor-Fletcher prodded the ball across goal and there was Kevin Phillips to bundle it home from a yard out.
Tangerines boss Ian Holloway introduced Nouha Dicko after 75 minutes and eight minutes later he fired the visitors ahead with a brilliant overhead kick.
Kevin Phillips chased a long ball over the top and as Amos went to close him down on the byline, the veteran striker chipped over a cross which was headed only as far as Dicko, who flung himself into the air to score a stunning winner.