Jake Livermore put Steve Bruce's side ahead after 20 minutes when his shot from outside the area took a deflection off Martin Skrtel past Simon Mignolet.
But the Reds were back level seven minutes later when skipper Steven Gerrard curled a free-kick around the wall into the net.
David Meyler then scored with 18 minutes remaining to give the initiative back to Hull and Tom Huddlestone's shot was headed into his own goal by Skrtel with three minutes remaining to hand the Tigers their first-ever win against the Reds and dent their title push.
The Reds were without the prolific Daniel Sturridge as he began what could be a stint of up to eight weeks on the sidelines after suffering ankle ligament damage in training on Friday.
Brendan Rodgers had recalled Victor Moses and Raheem Sterling, the latter making his first start since October 5, but they proved inadequate replacements for Sturridge.
For Hull, it was a memorable afternoon and a season's best performance - just the boost required after last week's defeat to lowly Crystal Palace.
The match quickly settled into a pattern of Liverpool going forward and Hull clearing their lines.
The Reds forced three corners in the first six minutes, but the hosts stood up well to Gerrard's delivery.
There were hints that Hull were not going to be completely passive, though, Yannick Sagbo and Livermore creating a promising counter-attack in the 14th minute only for Robert Koren to linger too long over a final ball.
Nevertheless, it was still a major surprise when Hull went ahead six minutes later.
Moses was culpable, giving the ball away to Ahmed Elmohamady when trying to attack from the back and bringing Livermore into the game. He exchanged a quick one-two with Meyler, advanced on goal and saw his 20-yard strike loop past Mignolet via a heavy deflection off Skrtel.
Hull's game plan would surely have been to grit it out until half-time with their lead intact but with 26 minutes gone Curtis Davies felled the advancing Jordan Henderson. Luis Suarez appeared interested but Gerrard pulled rank. It was a decision he would not regret, bending the ball brilliantly past Allan McGregor after Skrtel pulled away from the wall to create a gap for the shot.
The leveller settled Liverpool and both Gerrard and Suarez began to play with greater freedom as they probed Hull for further openings.
Yet they did not muster a shot of note between them until the stroke of half-time when Suarez hit an unusually tame effort from Sterling's clever through ball.
Liverpool started the second period shakily, Kolo Toure at times resembling an accident waiting to happen at the back.
The impetus was still on them to win the game but Moses and Sterling were offering little cutting edge in support of Suarez.
Hull threatened on the hour when Davies headed a Robbie Brady free-kick a yard wide of Mignolet's goal and the momentum began to tilt in the home side's favour.
Meyler was their next scorer, driving into the bottom corner after his initial strike was blocked by Toure, but Davies, Sagbo and Livermore all had a hand in the build-up.
Just before the goal McGregor made a brave close-range save to deny Moses, a contribution just as vital to the cause.
Suarez shot just wide with a long range free-kick as Liverpool pushed for a leveller, frequently leaving themselves exposed as they threw numbers forward.
A third Hull goal arrived when Sagbo found Huddlestone in the box. His chance to finally end a long goal drought - and go for the haircut he has promised to have when he next scores - was not taken as his shot looked to be heading well wide until Skrtel intervened and left Mignolet stranded to seal a historic win for the hosts.