Rollins and May closed with flawless rounds of 8-under 64 on a low-scoring day at Atunyote Golf Club.
Both players reached the par-5 18th green in two shots. May made his two-putt birdie first, then watched from the clubhouse porch as Rollins did the same to move one ahead.
There were still three groups to finish, but no one was within striking distance of Rollins, who ended at 19-under-par 269 for his first victory since winning the 2002 Bell Canadian Open.
'I'm in a little bit of shock right now,' admitted Rollins, who carded eight birdies in his final round. 'Obviously, to shoot 64 on Sunday and not make a bogey is pretty special anytime, especially when you can get a win out of it.'
Free of the back pain that plagued him for 2 1/2 years, May moved up from ninth place overnight with six birdies and an eagle at the par-5 12th.
The man who shot three straight rounds of 66 and lost in a playoff to Tiger Woods at the 2000 PGA Championship had a similar week here, opening with a 73 and then shooting 66-67-64 to get to 18-under-par 270.
'Unfortunately, I played so well I actually left some (shots) out there,' said May. 'I'm just happy to have my back back. I am able to swing a golf club again and do what I love.
'I'm happy. I went out and played a good, solid round of golf and was just one shot short.'
Japan's Shigeki Maruyama birdied the 18th to finish alone in third place at minus-17 after a round of 7-under 65. Omar Uresti was one of four players who shot a 64 and he shared fourth place with David Branshaw at 16 under.
There were low scores to be had on a perfect Sunday at Atunyote, which filled in for 35-year host En-Joie Golf Club after the Southern New York course was flooded by recent heavy rains.
Rollins took advantage of the scoring conditions early with three consecutive birdies beginning at the third hole.
He was 15 under around the turn and 18 under following another flurry of three straight birdies from the 12th, but Rollins didn't really win this tournament until the final two holes.
After finding a fairway bunker off the tee at the par-4 17th, he could only muster a shot into the heavy rough and well short of the green. But a good chip landed Rollins within 15 feet to set up a par-saving putt.
At the par-5 closing hole, Rollins went long off the tee and was 270 yards out. He landed his second shot on the green, where it trickled just onto the back fringe, and then putted within 6 feet.
The second putt was tricky, but Rollins found the center of the cup.
'Eighteen has been reachable all week,' he said. 'But to make that six-foot curler to win it...those last two putts were probably the best all day.'
His second PGA TOUR victory gave Rollins enough Ryder Cup points to move him into 10th place on the list.
With a showdown at the K Club looming just two months away and with point values doubled this year, it may be the most followed statistic on the PGA TOUR.
'I started the year off with a good start and fell into what a lot of guys fall into. They started watching the Ryder Cup points every week,' said Rollins, who also claimed $630,000 for his victory.
'Then all of a sudden I didn't play that well. I got away from watching and now all of a sudden I'm right back there again.'
Third round leader Gabriel Hjertstedt, the 1997 B.C. Open winner, managed only a 1-under 71 and led a group of six players who tied for sixth place at 15 under par.
Hjertstedt was joined there by Nicholas Thompson, who shot a 64, as well as Scott Gutschewski, Daisuke Maruyama, Matt Gogel and 1987 Masters champion Larry Mize.
Last year's winner, Jason Bohn, shared 12th place with Ryuji Imada and Paul Stankowski at minus-14.