The Northern Irishman looked at ease for much of the two-and-three-quarter-mile listed event before working his way into contention heading down the back straight.
McCoy was pushed all the way by Lost Legend, ridden by Richie McLernon, but a trademark late push sealed the historic victory.
His total is made up of 4,049 British jumps, 134 jump winners in Ireland and nine on the flat.
It was the latest milestone in a quite incredible 19-year career and, with 76 winners already this season, McCoy is on pace to become the first jockey to ride 300 winners in a season.
(Reporting By Tom Hayward; Editing by Rex Gowar)
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