The win is the first on the PGA Tour for Coceres, who has two victories on the European circuit. His last win came at the 2000 Dubai Desert Classic.
The players returned to the course at 8am ET to resume their sudden-death playoff. Lightning in the area on Sunday forced a one-hour weather delay and when Mayfair and Coceres finished tied at 11-under 273, there was only enough sunlight to play two playoff holes.
On Monday morning, Coceres missed the green with his second shot at the fifth playoff hole, No. 18, and landed short and left in a hazard. But he blasted out of the marsh four feet from the hole.
'There was a lot of grass behind it,' said Coceres, referring to his lie at the fifth playoff hole. 'You couldn't see it very well. The difficulty was not just putting it on the green, but putting it close to the hole.'
Mayfair hit driver into the fairway but narrowly missed the green with a 4-iron second shot. He played his third shot five feet past the hole and then missed his par save left.
That opened the door for Coceres. Earlier in the playoff, Coceres missed a three-footer to save par at this hole that would have won him the championship. This time Coceres ran it home for par and his first victory in the United States.
'I'm very happy,' said Coceres. 'But I had quite a few opportunities to finish it off.'
With the victory, Coceres pocketed $630,000 and earned a two-year exemption on the PGA Tour. He also joined Roberto de Vicenzo as the only Argentines to win on tour.
Coceres had the advantage on the third playoff hole. Both players made it to the fairway off the tee but Coceres was the only one to reach the green, as his ball landed 35 feet from the stick while Mayfair missed the green short with a 5-iron.
Mayfair played his third shot short of the hole by 15 feet and missed that par putt by two feet. Coceres lagged his birdie putt to three feet but missed the save to extend the playoff to hole No. 4.
Mayfair used a four-iron off the tee and came up 15 feet short of the target. Coceres pulled his second into a greenside bunker and only blasted his third to the fringe.
The honor belonged to Mayfair at No. 17 who had his birdie putt to win for the first time since the Buick Open in 1998 miss right. Coceres drained his par save from the fringe to force the fifth extra hole, where he won.
'I would have loved to have won, but I give him all the congratulations in the world,' said Mayfair, whose second-place finish is his third top-10 of the season. 'I'm happy with the week, I'm happy with my year so far.'
Both players matched each other with pars during Sunday's first two playoff holes. Coceres had 15 feet for birdie at the second playoff hole, but he never even touched the cup with his putt.
Carl Paulson, Bernhard Langer, Scott Verplank and Vijay Singh shared third at minus-10.
Steve Flesch, Mark Brooks and Davis Love III, a four-time winner of this event, finished tied for seventh at 9-under 275.
Full-field scores from the WorldCom Classic