Snedeker briefly regained a one-shot lead with a birdie at the par-five 16th, where he rolled in a 10-foot putt. "I was proud of how I played". But Tway and Ryan Moore hung around, and when Moore birdied 18 and Tway the 17th and 18th, the three went to extra holes to decide the matter.
Tway had looked an unlikely victor earlier in the day as Snedeker increased his third-round lead from three shots to five during a solid front nine.
His father, Bob Tway, was an eight-time victor on the PGA Tour who captured the 1986 PGA Championship by sinking a bunker shot on the last hole to defeat Greg Norman.
Tway's two late birdies gave him a 1-under-par 71 and a 72-hole total of 14-under 274, while Moore sank a nine-foot putt on the 18th hole for his third birdie on the last four holes of regulation to equal that score. "I played a really good front nine in tough conditions, made the turn and actually drove the ball really well, just hit some really, really poor iron shots".
Starting his 19th full season on the tour, Baddeley, 37, could not quite add to his four victories there but added $241,280 ($A342,000) to his $US20,543,617 in career earnings while some younger countrymen also impressed.
"I think he's probably crying, to be honest", Kevin Tway said of his dad. "It's been a long road and this is why you work so hard, what happened right there".
Moore also birdied the first two playoff holes to stay alive, but he missed his birdie attempt at No. 10 before Tway sank the victor. Troy Merritt carded a 68, Sam Ryder and Australian Aaron Baddeley fired 69s and Web.com Tour graduate Im Sung-jae of South Korea posted a 71 to complete the group at 13-under.