The 45-year-old Fijian closed with 1-under-par 70 to match Garcia (70) and Kevin Sutherland (68) at 8-under 276 on the sun-baked Ridgewood Country Club course, the first-time site after 41 years at Westchester Country Club.
Singh, the 1993, 1995 and 2006 winner at Westchester, earned 11,000 FedEx Cup points in the playoff opener to take the lead with 109,500 points — 5,125 ahead of second-place Garcia. The WGC-Bridgestone Invitational winner three weeks ago at Firestone, Singh also earned $1.26 million for his 33rd PGA Tour victory.
Garcia and Singh made long birdie putts on the first extra hole, the 472-yard 18th framed by a canyon of trees, with Garcia rolling in a 27-footer and Singh matching him moments later from 26 feet. After driving into the right rough, Sutherland was on the back fringe in three but couldn't match Garcia and Singh's birdie effort.
Garcia and Singh then moved to the 577-yard, par-5 17th. Garcia hooked his drive into the left rough, just feet from towering trees. With Singh in the middle of the fairway, Garcia hit his second shot behind a tree in the right rough. Singh then hit a 267-yard approach onto the green, about 20 feet long and right.
Because the gnarly ground around Garcia's ball was ruled abnormal, he was able to take a drop that allowed him to get a clear shot to the green. He advanced the ball near the front of the green about 30 feet from the hole and nearly holed his chip.
Singh then rolled his 20-foot eagle putt within inches for a tap-in birdie.
Third-round leader Kevin Streelman (72), Ben Curtis (68) and Mathew Goggin (67) tied for fourth at 7-under, and Martin Laird (67), Justin Leonard (67), Nicholas Thompson (67), Mike Weir (72) and Paul Casey (72) followed at 6-under.