Alderwood's chance looked to have gone when the he was hampered coming round the final bend, but he soon recovered to put in his winning bid.
The 20-1 shot, trained in Ireland by Tom Mullins and owned by McCoy's boss, JP McManus, jumped the last in great style and battled on resolutely up the hill.
Alderwood clinched victory by three-quarters of a length from Edgardo Sol (25-1), with Sailors Warn (16-1) a head back in third and Plan A (20-1) not far away in fourth.
McCoy said: "It's great to have a winner at last.
"I rode him the last day (at Leopardstown) and he was going well until the second-last but then didn't finish as well as I'd have liked.
"I think he's had a fibrillating heart problem.
"He got murdered on the bottom bend but he was 20-1 so I was taking a few chances and hopefully he would keep going.
"It's great to ride a winner for my boss."
The winning trainer is part of the Mullins family dynasty and is Ireland's champion trainer Willie's brother.
He said: "It's great to have a winner here at last, what with my father and two brothers already on the list.
"Things didn't quite work out for him the last day but he had been working very well at home.
"He got absolutely hammered on the home turn but it makes a difference having the right man on board and he really is the 'Real McCoy'.
"It's such a delight having him on board and the owner, JP, is such a nice man."
McCoy added: "It got a bit tight for room when we turned in, but it was more fighting your corner than anything and with that many runners there's always going to be a bit of trouble.
"I tried to save as much ground as possible and he picked up well.
"If I'm honest, I came here more with hopeful rides than anything but you've always got to believe you'll have winners."
McManus, who was having his third winner of the week following victories for Alfie Sherrin and Sunnyhillboy, said: "It's nice to see Tony get off the mark.
"When you've had a week like this you wish it would keep going."