Singh closed with a 2-under 70 to join Daly at 13-under-par 275. Daly posted a final-round 67 to forge the extra session.
Singh hit an average second shot leaving himself 50 feet for birdie. Daly's third flew the green. He pitched on to 10 feet, but it didn't matter.
Singh rolled his putt within 2 feet of the cup and kicked in his par putt for the win at Redstone Golf Club.
'It was a tough day for me,' Singh said. 'The way I started off, not making any birdies and putting myself in the positions to make birdies and never getting any. I played really solid and I'm really pleased with the way I hung in there and never gave up. Fortunately for me nobody came out of the pack except for John and kind of made a run at it. It was a good way to finish.'
Jose Maria Olazabal, who lost in a playoff three weeks ago at the BellSouth Classic, posted a final round 70 to take third place at 11-under-par 277.
Darren Clarke, who tied for second last week at the MCI Heritage, carded a 5-under 67 to share fourth with Greg Owen at 10-under-par 278. Joe Ogilvie finished one stroke further back at minus-9.
Singh opened the final round with a share of the lead alongside Gavin Coles. The Fijian bided his time while Coles and Owen both moved out in front.
'On a day like today, you're not making any putts, the only thing that can get you is when you hit one bad shot and short side yourself and come out and make bogey,' said Singh, who picked up $900,00 for his 26th tour win. 'Then you say, 'man, I played well and I missed one shot and I made a bogey.'
'I wasn't going to do that. I played to the pin or just away from the pin where if I did hit a poor shot, I'd have a decent putt at it and it worked.'
Both Coles and Owen would falter however. Singh was steady with 13 consecutive pars to open his round. He dropped his second shot within 5 feet of the cup at the par-4 14th.
Singh rolled in that birdie try to get to 12 under par, one shot clear of Daly and Jeff Maggert. Daly briefly joined Singh in the lead with a birdie on the 17th.
The reigning PGA champion responded with a two-putt birdie from the fringe at the par-5 15th to regain the lead. He parred out to remain there.
Daly opened with a birdie on the first. He got to 10 under with a birdie on the fourth. Daly then went bogey-birdie-bogey over his next three holes to make the turn at minus-9.
The two-time major winner got to 10 under with a birdie on the 12th. Daly's birdie at the 15th briefly gave him a share of the lead. He ran home a birdie putt at the 17th. Daly forced the extra session with a 10-foot birdie putt at the last.
'Nothing was going too good on the putter on the front nine, I missed a lot of short putts,' Daly said. 'But the way I finished, I'm proud of myself for coming back like that and hitting some shots when I needed to. I wished I would have done better in the playoff.'
Coles played the back nine in four-over to finish at 8-under-par 280 after a final-round 75. He was joined there by Brian Davis (70), Lucas Glover (67), Kent Jones (71), Maggert (71) and Bo Van Pelt (70).
Billy Andrade, Doug Barron, Carl Paulson and Charles Warren finished one stroke further back at minus-7.