The 5/1 shot finished strongly under Joseph O'Brien to win by a length from outsider Foxtrot Romeo (33-1) with Reply (25-1) third.
It was a dramatic turnaround for the son of Oasis Dream who was second last in the English equivalent at Newmarket.
Power is owned by the Coolmore team and John Magnier said: "The ground makes a big difference to him. He didn't have to have fast ground last year, but he'd been working well since we got good ground and he just got stuck in the mud at Newmarket.
"It looked like Daddy Long Legs would win but I think Power has to be ridden to come late, I think that's something they have learnt about him."
Richard Hannon's Trumpet Major, fourth at Newmarket, was the 9/4 favourite but finished last whilst French colt Hermival - third at HQ - was only sixth.
Overnight market leader Parish Hall missed the race with a leg infection and Jim Bolger's charge will also miss next week's Investec Derby at Epsom.
In the race of the day in England, 2/1 favourite Bated Breath won the Temple Stakes at Haydock.