Haye, 37, pledged to move away from the gung-ho approach that contributed to his debilitating setback last time out and he did enough to pocket the first two rounds, prevailing in a battle of contrasting jabs - the older man's slung low as Bellew popped out his firm lead in orthodox fashion.
Bellew - just two years younger than Haye at 35 but whose boxing, fitness and prospects are on a decidedly more upward curve - played the ideal waiting game to dismantle the former world cruiserweight and heavyweight champion on Saturday night.
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Bellew nearly knocked down Haye in the fourth round, but managed to do so in the fifth round. Haye connects with a couple of short left uppercuts that momentarily put Bellew to the ropes.
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A second knockdown followed moments later and Bellew - the underdog with bookmakers, as he was in the previous fight - delivered a pinpoint left hand in the fifth to again send Haye down. Tony Bellew, I take my hat off to him, boxed a great fight, and I didn't.
The holder of all but one of the heavyweight belts is discussing a $50million offer to fight WBC champion Deontay Wilder, but would be willing to meet Haye first if that deal continues to stall.
"When I saw him in the first fight it was very upsetting. Just let me get past 1.30pm on Sunday when her flight touches down and I'll try and talk her round".
I just want to punch him. Whatever you say about Haye, he grew old in there tonight. In round 11, the bout was stopped after Haye fell out of the ring.
Asked if that was the end of his career, Haye replied: "I don't know".
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Meanwhile, Bellew has options to fight big names at heavyweight or return to cruiserweight where he has already talked about taking on undefeated (although now retired) superstar Andre Ward.
He said he would meet British former world champion Fury at heavyweight but only if the bout happened soon.
"I would beat Andre Ward".
"He's a better fighter, a legend of the sport". "I won't go on too long, but I ain't stopping now". Haye throws another combination and both men then taunt each other at the same time.
Rising unsteadily, Haye could not keep Bellew at bay, and seemed to have aggravated a leg injury as he crumpled to the canvas after another flurry of shots.
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