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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."

Emmerson Whittel may need surgery on his jaw, while the club alleges player Josh Lynam was also bitten on the ear.
The RFL's match review panel will look at official video on Thursday, as it does for all on-field incidents.
Keighley have gathered additional video from spectators following an appeal.
Footage already online, shot from the stands, shows a number of fights breaking out on the field between the two sets of players.
Following the incident, Whittel posted on Twitter that brackets and bands had been used to try to re-align his jaw and that he faces at least three months out.
Keighley Cougars of League One, England's third-tier competition, progressed to the Challenge Cup fourth round with a 50-32 win over Fryston Warriors - a side from the second tier of England's amateur game.
The match, a "home" game for Fryston, was played at nearby Featherstone in West Yorkshire after the tie was at risk of being reversed and played at Keighley instead.
Keighley have also complained to the RFL about their off-field treatment before kick-off, as they allege players and members of staff were refused entry to the ground without a valid matchday ticket.
A statement on Keighley's website said: "The players' allocation of 'family and friends' tickets was then claimed to have been used to admit the playing squad and coaching staff into the ground.
"The club is outraged by this development."
The BBC contacted Fryston Warriors, who have declined to comment at this time.

Naz Shah has apologised for sharing the graphic showing Israel's outline superimposed onto a map of the US with the comment "problem solved".
It was shared in 2014, before she became Bradford West MP.
The Board of Deputies said the post, highlighted by the Guido Fawkes political website, was "appalling".
The graphic said relocating Israel would be a "solution to the Israel-Palestine conflict", and that it would allow Palestinians to "get their life and their land back".
In a statement, Ms Shah said: "This post from two years ago was made before I was an MP, does not reflect my views and I apologise for any offence it has caused."
Labour confirmed she had stepped down as Parliamentary Private Secretary - an unpaid backbench assistant - to shadow chancellor John McDonnell.
In a second statement, the MP said: "I made these posts at the height of the Gaza conflict in 2014, when emotions were running high around the Middle East conflict.
"But that is no excuse for the offence I have given, for which I unreservedly apologise."
She said she would be expanding her "existing engagement and dialogue with Jewish community organisations and will be stepping up my efforts to combat all forms of racism, including anti-Semitism".
The Board of Deputies of British Jews said the comments were "simply appalling", calling for an urgent meeting "for clarification of her views on Israel and the UK Jewish community".
AP McCoy won his first race of his final Cheltenham Festival on day three, riding Uxizandre to victory in the Ryanair Chase.
[NEXT_CONCEPT]
Keighley want the Rugby Football League to consider amateur video footage when they review a brawl during the club's Challenge Cup tie against Fryston, which left a player with a broken jaw.
[NEXT_CONCEPT]
A Labour MP has stepped down as an aide to the shadow chancellor over a Facebook post suggesting Israel should be moved to the United States.