All the posturing was forgotten in the third round as Bellew floored Haye heavily in the corner when they traded hooks at close range.
Haye (28-4, 26 KOs), once the most exciting heavyweight in the world, was left flat on his face in the fifth round.
David again showed heart and desire to fight on, got up and attempted to do so before being pinned back on the ropes by Bellew.
But Saturday's bout at London's O2 Arena rarely looked like lasting as long. Injuries and a stop-start career have taken their toll on the 37-year-old, and Bellew exposed those truths for the second successive fight.
"I'm a walking Super Series - every fight I'm in is the Super Series!" But speed decreases with age.
"I lost my brother last year and there is only one person this victory is for - it's for Ashley", said 35-year-old Bellew, clearly emotional and raw after the tragic events of August 2017.
With Bellew forcing the pace and applying the pressure, it was clear to see that Haye was struggling to match the pace and deal with the sharp and precise shots being thrown at him by the Merseyside fighter. Haye tried to force the action a lot more in the final minute, missing wildly with a combination in chasing Bellew who used his feet to avoid the punches. "I will have to review it", he said.
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At the time, sources said Bruns suffers from seizures and may have been foaming at the mouth after the crash. She also was charged with a red light violation of disobeying a traffic device.
The opening round was a nip and tuck affair with both men content to lead off with the jab, however, David's jab was sharper and landing with much more spite in comparison to Bellew's.
"Me and Dillian [Whyte] have had words over the years", Bellew said post-fight.
"We were going for the knockout and we gave you fireworks and I'm glad we gave everyone a good fight and a good night". He boxed a great game-plan, and I couldn't quite get to it. Everything happens for a reason. He's a great champion, and I enjoy the battle. We are a similar stature and that's why we put on a great fight.
"He's a better fighter, a legend of the sport". Bellew, who like Haye is a former world cruiserweight champion now operating at heavyweight, is ranked No. 7 with the WBC, and there is no obvious next opponent for him.
The Liverpool fighter dedicated his victory to his late family member before claiming he would like to fight former pound-for-pound king Andre Ward.
A few days ago I predicted that if David Haye could come into the contest fully fit, focused and injury free, that he would be more likely to win the rematch. "What feels like went wrong, was Tony was better tonight".