Ryan Palmer, who made the turn with a one-shot lead, hit the water twice for a triple bogey on the par-5, 552-yard 15th, while his playing partner Holmes sank a 14-footer for an eagle. Holmes' one-shot lead expanded to six, and the tournament was decided.
Palmer finished in a five-way tie for second at 14-under 270. Steve Lowery, J.J Henry, Camilo Villegas and Scott Verplank also were 14 under.
Defending champion Phil Mickelson birdied five of the last six holes, the last four in a row, to finish tied with Justin Leonard and Jonathan Byrd at 13-under 271.
Holmes, the top finisher in last year's PGA qualifying tournament, is the first rookie to win a tournament since Sean O'Hair won the John Deere Classic last July. O'Hair was the only rookie to win last year.
On the 15th, Holmes reached the green easily in two with a 263-yard four-iron blast over the water, then sank the 14-footer to go to 20-under. Palmer, meanwhile, twice hit the water and got a triple-bogey, tumbling from 17 under to 14 under.
Palmer's tee shot landed on the fairway, then bounced downhill into the water, scattering birds along the way. After his drop, Palmer again hit the water. He dropped again, got on the green and three-putted to end any hope for his second PGA tour win.
Holmes, meanwhile, hit his tee shot 300 yards down the middle of the fairway, then cleared the water with a beautiful second shot. After the 14-footer, Holmes pumped his fist in triumph.
Palmer made the turn with a one-shot lead after rolling in a 7-foot downhill putt for birdie on the par-4 ninth hole. But Holmes, who led by one entering the final round, birdied the 10th to tie it.
On the par-4, 469-yard 11th, Palmer hit his tee shot into the water. The subsequent bogey dropped him to 16 under and put Holmes in front for good.
Holmes birdied the 17th, and with a seven-shot lead, blasted his tee shot 354 yards on the 18th, then slapped hands with fans inside the rope as he walked down the 18th fairway.
A crowd of 82,150 attended the final day, bringing the best-attended PGA event's total to a record 536,767. The crowd was about half the size of the one that created a raucous party atmosphere on Saturday. It was a more subdued group, too, but still far more lively than the average PGA gallery.