Snedeker was the first to be eliminated with an opening par, while Moore and Tway swapped birdies for the first two playoff holes.
"I'm kind of at a loss for words". 10-12, Snedeker appeared to steady the ship with a 10-foot birdie on the 16th hole that put him one ahead of Moore and, at the time, three ahead of Tway with just two holes to go.
Brandt Snedeker held a five shot lead with 11 holes to play but suffered a back-nine collapse which opened the door for Tway and Moore.
"I have to find a way to win today", Snedeker tweeted.
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", said Tway of his father, who had been watching on television.
"I played well on the front nine, but lost it on the back", said Snedeker, who was seeking his 10th PGA Tour victory. "He's pretty proud of me". "It's been a long road and this is why you work so hard, what happened right there".
The 20-year-old finished regulation at 13-under 275, after carding a 71 in the final round with four birdies against three bogeys.
The nine-time PGA Tour victor bogeyed the first three holes on the back nine, birdied the par-5 16th, bogeyed the par-4 17th and parred the 18th, missing from 9 feet.
Aaron Baddeley, who earned a spot in the tournament through the Monday qualifier, birdied the last hole to shoot 69 and finished one stroke back in a tie for fourth with Luke List (67), Troy Merritt (68), Sam Ryder (69) and Sungjae Im (71) of South Korea.