Palmer closed with a 10-under 62 to finish the event at 22-under-par 266 for his first PGA Tour title.
'It's just unbelievable. What a week, what a day,' said Palmer, who picked up $756,000 for the win. 'To play the way I did today and come out on top, what a feeling. I've never shot 62 in the final round. Never in my career had I shot it. Its just the second time in my career I had 10 birdies.'
World No. 1 Vijay Singh, who won this event last year, closed with a 5-under 67 to finish at 19-under-par 269. He shared second place with third-round co-leader Briny Baird, who posted a final-round 70.
Cameron Beckman and Joey Sindelar were one stroke further back at minus-18. Tom Lehman, who shared the third-round lead with Baird, closed with an even-par 72 to end at 17-under-par 271.
Palmer, a tour rookie, opened with a birdie at the first and came right back with a birdie on two. After a par at three, Palmer birdied No. 4 on the Magnolia Course to move to minus-15.
The Texas A & M alum sank a birdie putt on five to keep his roll going. Palmer made it three straight, and birdies on five of the first six holes, as he sank his birdie putt on six.
With that last birdie, Palmer tied Baird and Lehman for the lead. Palmer cruised around the turn with five straight pars before turning it on again.
Palmer stuck his second shot within 2 feet of the cup for birdie at the 12th. That birdie again tied him for the lead at minus-18. He quickly jumped two shots clear of the field with birdies at the 14th and 15th.
Palmer, who won on the Nationwide Tour in 2003, made it three straight as he dropped his second shot within a foot of the cup on No. 16. The 28-year-old kicked in that birdie and made it four straight as he drained a 50-foot birdie putt on 17.
Palmer left a birdie putt just short of the cup at the last, but he tapped in for par. Then it was off to the clubhouse to watch the final eight groups come in. No one was able to catch him and it was off to the winner's circle for Palmer.
'My caddie and I figured 20 under was a good number to get to and that was my main goal,' Palmer said. 'I've been hitting the ball good all week. I finally got some putts to go in. Winning last year was a lot of confidence for me coming into this year. I played in Australia over the winter and had some good success over there. I had the confidence and the game, it was just a matter of proving it to myself.'
Singh, who battled his swing on Friday, worked out the kinks on the range after that round. He closed with rounds of 65-67 to move into second place.
The Fijian moved into red figures Sunday with birdies at four and five. However, Singh tripped to a bogey at the sixth. He fought right back to birdie the next to get to 16 under.
Singh ran off four birdies in a five-hole stretch from the 10th to jump to 20 under. He was within two strokes of Palmer, but could not get any closer.
Singh fought a balky putter down the stretch. That included a three-putt bogey on the 16th, but he parred his final two holes to share second.
'I made a few mistakes early with a bogey at six and a bad drive at eight,' said Singh. 'I thought I played well though. I tried to make that putt on the last and dragged it left a little. I'm looking forward to next week because my game is coming back.'
Baird opened with six straight pars before a birdie at seven. He moved to 19 under with a birdie at the 11th. Baird got within two of Palmer with a birdie at 14. Like Singh, Baird bogeyed 16 and parred the final two holes to finish three off the pace.
Lehman was joined in a tie for sixth at minus-17 by Mark Hensby (68), Mark Calcavecchia (69) and Tim Clark (69). Lucas Glover, John Huston, Neal Lancaster, Geoff Ogilvy, Carl Pettersson and Vaughn Taylor ended one stroke further back at 16-under-par 272.