The six-shot win was the second largest margin of victory in tournament history. Steve Elkington won by seven in 1997.
'I think I get to relax a little bit more now,' said Ames, who at 41, tied for the second oldest champion. 'It's a player's goal to either win majors or play in majors. I'm going to enjoy it.'
Goosen birdied the tough 18th to shoot a 3-under 69.
Jim Furyk, the first- and second-round leader, shot a 1-under 71 on Sunday and tied for third place. Tour rookie Camilo Villegas (71), Pat Perez (71) and Henrik Stenson (73) matched Furyk at 5-under-par 283.
Tiger Woods struggled to a 3-over 75 on Sunday and never factored into the tournament. He tied for 22nd place at 1-over-par 289, 15 shots behind the man he pummeled 9-and-8 in the opening round of the WGC-Accenture Match Play Championship.
The Stadium Course at the TPC at Sawgrass played difficultly again on Sunday. There were eight scores in the 80s in the final round, as opposed to three in the 60s.
That just made Ames' spectacular round and margin of victory all the more impressive.
'Tough conditions and a Sunday on a difficult golf course, where the greens were just right on the limit - I think he played awesome,' said Sergio Garcia, who was one off the lead with the final round to play, but struggled to a 6-over 78 for a share of 14th place.
Ames began the final round with a one-shot lead over Vijay Singh and Garcia, both of whom are ranked in the top 10 in the world. Singh and Garcia played poorly out of the gate on Sunday, but Ames held tough.
He parred the first, but kicked in a 3-foot birdie putt at the second to move three clear of the field. Ames rolled in another 3-footer for birdie at six to reach 11 under par and move four ahead of Goosen.
Ames had decent looks at birdie at both the seventh and ninth holes, but failed to convert. He held a four-shot lead as he headed to the back nine, but the only hiccup of the round awaited Ames.
At the par-4 10th, Ames' approach landed in a bunker and he had an awful lie against the lip. His blast hit the mound in front of him and fell back into the sand. Ames knocked his fourth to 10 feet, but came up short on his bogey. He double-bogeyed the hole and was suddenly only two ahead of Goosen.
Ames rebounded in style with a 12-foot birdie putt at the 11th. At the par-3 13th, Ames hit an 8-iron inside 2 feet to set up another birdie and now he was five up thanks to some miscues by Goosen.
Goosen birdied 16 to get to minus-7, but Ames buried a 9-foot birdie putt at the 15th to reclaim his five-shot lead.
At the par-5 16th, Ames' drive landed in the first cut of rough on the right side, which gave him a great angle at the flag. He decided to go at the pin with a 5-iron and the ball barely made it over the water. Ames' second stopped on the fringe 25 feet from the hole and he converted the eagle putt to move ahead by seven.
'It was only a 5-iron. It wasn't a 3-iron or 2-iron,' said Ames. 'I hit the shot exactly how I pictured it. The wind switched on us. It ended up being a good eagle.'
Despite being armed with a seven-stroke cushion, Ames still had to negotiate the par-3 17th and par-4 18th. Those two holes took five shots away from Arron Oberholser on Saturday as he went six-six.
Ames headed to the famous island-green 17th. He played safely away from the front-right hole location and hit his tee ball 65 feet left of the flag. He ran his downhiller 6 feet past the cup, but made the comebacker.
Ames hammered his drive down the center of the fairway at 18 and went at the pin with his approach. It stopped 25 feet short of the hole where he two-putted. Goosen birdied the hole ahead of him so Ames missed out on a tournament record.
'I really enjoyed the day,' said Ames, who lives in Canada, but is from Trinidad & Tobago. 'It felt almost like a walk in the park the way I was hitting the ball. It was a good day. Good week.'
Two-time Masters champion Jose Maria Olazabal posted a 1-under 71 and took seventh place at minus-4.
Ernie Els (71), Vaughn Taylor (73), Bo Van Pelt (74), John Rollins (74), Carl Pettersson (74) and Singh (77) tied for eighth place at 3-under-par 285.