Kaye, who picked up his first PGA Tour victory, birdied the 18th hole to tie Rollins at minus-13 and force the playoff. Rollins had birdied each of the last two holes to finish at 13-under.
'I've worked really hard on my game, and it's a really gratifying feeling to come out on top,' said Kaye. 'You know, sometimes you can play your best and it's still not good enough out here, and I've done that a few times.
'You just try to take what you can from it and chalk it up as another experience and put it in the Rolodex and hopefully some day you get to recall that when you need it.'
The two men, who shared the lead after three rounds with two others, returned to the 18th tee for the first and only extra hole. Kaye bombed his drive right down the middle while Rollins pulled his drive into the trees on the left side. Rollins was able to fix his lie as the ball plugged.
Rollins knocked his second shot down the fairway. Kaye on the other hand ripped his second shot from 251 yards out onto the fringe about 18 feet from the cup.
'I just knew if I hit it good, I couldn't hit it over and it would be all right,' said Kaye.
Rollins dropped a sand-wedge onto the green with his third shot and two-putted for par. Kaye calmly stood over his eagle putt and rolled it home for the victory. Kaye previously had five second-place finishes before earning his first title.
Briny Baird and Skip Kendall were also tied for the lead heading to the final round when third-round action was completed Sunday morning after rain halted play Saturday.
Baird struggled badly in the final round with two birdies and two bogeys on the front nine. Around the turn, it was all downhill for Baird. He bogeyed four out of five holes from the 11th and double-bogeyed the par-3 16th for a final-round, 6-over 77.
Kendall faired slightly better. He carded four birdies and two bogeys on the front side, before two more bogeys and a birdie around the turn. After a 1-under 70, he finished at 10-under-par 274 in a tie for fourth.