The Liverpudlian, 34, pounced when Haye hurt what turned out to be an Achilles injury in the sixth round to score a knockdown.
Haye, who had his right beam strapped, carried on as bravely as he could for the rest of the fight but was unable to move freely as Bellew seized the momentum.
And on the 11th, a second knockdown saw former heavyweight champion Haye revealed in the ropes, the towel enter from his corner and his hopes of a return to the world-title level of the sport left in tatters.
Bellew - a big underdog with bookmakers - compete to trainer Dave Coldwell in celebration as he scored a victory which will likely filter through to non-boxing fans far more than his 2016 world title win at Goodison Park did.
The first round had those in the O2 Arena interest. A hate-fuelled slug-fest or artistic boxing?
The latter won the day, with Bellew happy to see Haye jump in while he fired off solid replies in-between darting out of trouble.
And so set a pattern, Haye taking the center of the ring, Bellew nearer the ropes. slipping shots can be a dangerous game and a straight right to Bellew's jaw in the fifth was clear ringside, though nothing could be heard in the sixth as the Arena screamed at the drama.
Both men went down though neither faced a count as their falls to the canvas were considered slips but the sheer punch volume from Bellew then legally felled Haye, who looked stunned and shattered in answering a nine count.
Bellew, who stressed his opponent would start tiring after four rounds, was then able to dominate, dictating the pace and notably throwing everything at Haye in the seventh in an try to bring an end to proceedings.
Haye's blow in the ninth summed up his increasing agony and, two rounds later, his brave contradiction was ended moments after a barrage of punches sent him sprawling through the ropes.
Having scramble back into the ring, finally, his camp threw in the towel, signaling the third defeat of a 31-fight career.
'I've beaten one of the best'
Bellew sad He's probably the hardest puncher in the world, and he's so quick early on, he's like a sprinter. He can really hit but he can also take a few himself. He made the same mistake everybody else does.
'It felt like a Rocky movie
David Haye, also speaking I've knocked out guys a lot bigger and stronger but he has the heart of a lion. I gave my best and it wasn't good enough. He was by far the better fighter. He dug deep and took my best shots and put me down.
"I would love to do it again, I have never been in a fight like that. If the fans want to see it again I would do it again. We'll do it on his terms, -he deserves it."