Quinney birdied three in a row from the 15th to post 5-under 67 and get into the clubhouse at 16-under-par 272. Snedeker eagled the last to also end at minus-16 thanks to his own round of 67.
They returned to the par-5 18th for the first playoff hole. Both players found the green in two, but Snedeker had 40 feet for eagle. He was unable to sink that putt, but tapped in for birdie.
Quinney also had a lengthy eagle putt, which he was unable to make. When he tapped in for birdie, it was back to the 18th at Somerby Golf Club for a second time.
The duo each ripped drives right down the middle on the second extra hole. Snedeker, playing first from 207 yards out, knocked his approach to 12 feet.
Quinney, from a few yards closer, left his approach just short of the green, but on the fairway. He pitched his third to 8 feet.
Snedeker's eagle try slid by the left edge, but he tapped in for birdie. Quinney needed to make his 8-foot birdie putt to extend the playoff, but he pulled it and the putt didn't touch the hole.
The win for Snedeker was his first on tour and moved him to 1-1 in extra sessions, having lost to Kyle Reifers two events ago at the Chattanooga Classic.
'This is awesome. I'm kind of tearing up now since I've done so much work over the last year to get here. I feel like I played great today,' said Snedeker, who earned $99,000 for the win. 'I feel bad for Jeff 'cause he played a great last round. I was through that two weeks ago, so I know how he's feeling.'
Kyle Thompson, who was one of four players sharing the lead entering the final round, carded a 2-under 70 to share third place at 14-under-par 274. He was joined there by Tim O'Neal, who closed with a 3-under 69.
Justin Bolli took fifth place at minus-13 with a final-round 70. Jason Caron (70) and Jon Turcott (70) were one stroke further back at 12-under-par 276.
Quinney, the 2000 U.S. Amateur champion, carded birdies on the fifth and eighth to make the turn at 13 under. He parred the first five holes of the back nine before birdies on each of his next three holes got him to 16 under. Quinney parred the last to get into the clubhouse first.
Snedeker opened with back-to-back birdies from the first to move to 13 under. He gave a stroke back with a bogey on six, but recovered that lost stroke as he birdied No. 9.
The 25-year-old Snedeker tripped to another bogey on the 11th. However, he birdied 15 and 16 to get back to 14 under. At the last, Snedeker poured in a clutch eagle putt to join Quinney at 16 under and get into the playoff.
'It's nice to be on the winning end,' admitted Snedeker. 'I can breath a little easier the rest of the year. Hopefully I won't have to stress out the next couple of months and kind of enjoy the moment a little bit.'
Bryce Molder, who shared the lead entering Sunday with Thompson, Turcott and Mike Perez, stumbled to a 1-over 73 in the final round to end at 11-under-par 277. He was joined there by Michael Harris, Jin Park and Gary Christian.