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The Alan King-trained seven-year-old, a 16-1 shot, led all the way for the 19-time Champion jockey, who is retiring this season.
Ma Filleule (5-1) was second with 5-2 favourite Don Cossack third.
McCoy said: "I would love to say it's a relief, but I actually got such a thrill riding him."
The Northern Irishman did not seem to fancy his chances much pre-race, but trainer King's seven-year-old put in some spectacular leaps on the way round.
"I was actually thinking I wouldn't mind riding the horse in next year's Champion Chase," said McCoy after his victory.
"He ran away with me for a mile and a half and I thought he would never keep it up but I was quite happy coming down the hill."
McCoy's wife Chanelle and several of his family members were waiting in the winner's enclosure to greet him after his victory.
"He wanted that feeling one more time," said Chanelle.
"Heading into day three he wanted one more time to ride a winner at Cheltenham, to soak up the atmosphere and not finish his career without one more winner."
AP McCoy won his first race of his final Cheltenham Festival on day three, riding Uxizandre to victory in the Ryanair Chase.