My Tent Or Yours, at 16-1 and also trained by Henderson, finished second, with Petit Mouchoir (6-1) third in the opening day's feature race. The 9-4 favourite Yanworth finished seventh.
"It's fantastic. To win one was great, to win two is special," said Fehily, who won the Champion Hurdle on Rock On Ruby in 2012.
Buveur D'Air was Henderson's 57th career Festival triumph and owner JP McManus's 50th winner.
"All records are there to be broken. It's the horses and the people that make it. It's rather surreal really," Henderson, who also had a winner earlier with Altior in the Arkle Challenge Trophy Novices' Chase, told the BBC.
(Reporting by Alan Baldwin, editing by Mark Trevelyan)
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