Wearing the Grand National-winning colours of JP McManus, McCoy was at his strongest to take the valuable handicap chase at odds of 22-1.
McCoy only came in for the ride after his original mount, Dancing Tornado, was a late withdrawal.
He got the verdict on Tom Taaffe's charge by half a length from the brave Themoonandsixpence.
Majestic Concorde, the 3-1 favourite, finished third, while top-weight The Fonze ran a huge race in fourth.
McCoy always had Finger Onthe Pulse near the pace and took him into the lead some way out.
A melee at the final fence cost several horses their chance but up front Taaffe's nine-year-old had to overcome the persistent challenge of Themoonandsixpence (7-1) to land the main race of the seven-day Festival in the West of Ireland.
McManus said: "What do I have to say about the jockey? Tony is Tony. You have a bit of an edge when you have Tony with you."
Taaffe added: "Tony gave him a fantastic ride. That's why he is who he is.
"I feel a little sorry for Mark Walsh (original jockey for Finger Onthe Pulse).
"He has schooled him recently and was due to ride him, but things fell into place for Tony and it will be Mark's day another day."
The rest of the meeting once again belonged to Dermot Weld, who secured another three winners to take his tally to nine for the meeting.
Endless Intrigue set the ball rolling when coasting to victory in the www.thetote.com Maiden.
Twice successful in bumpers, the six-year-old had no difficulty in taking this prize for Robbie McNamara.
"He did it very nicely. Robbie was, as usual, in the right place at the right time and he made it easy," said Weld.
Seven later became eight when Rock Critic, the 7-2 favourite, fairly bolted up for Pat Smullen in the Tote Trifecta Rollover Handicap.
Weld added: "He was at his best behaviour and I was delighted to be drawn wideish with him.
"He will run again at Naas on Monday."
The unstoppable Weld then chalked up his ninth winner when the Smullen-ridden Unaccompanied (13-8 favourite) claimed the concluding maiden.
Kevin Manning had earlier worked the oracle aboard New Magic (4-1) to win the www.totegoracingclub.com Handicap.
Trainer Jessica Harrington reported: "We will step her up to 10 furlongs later in the year."
Hoopy (8-1) gave trainer Gordon Elliott a first victory at the Galway Festival when holding off King Of Redfield and surviving a stewards' inquiry in the Tote Jackpot Races 3 To 6 Handicap Hurdle.
However, Shark Hanlon, trainer of the runner-up, later announced he would be appealing the decision.
Novel Investment (10-1) proved a shrewd bet in the Tote Telebet 1850 238 669 Handicap Hurdle, while Ballyadam Brook completed a hat-trick with a clear-cut success in the Tote Placepot Races 1 To 6 Novice Hurdle.
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