Johnson managed an even-par 72 in the final round and finished the tournament at 13-under-par 275 to become the third player in tournament history to make this tournament their first win on the PGA Tour.
Johnson held a one-shot lead over Mark Hensby at the par-5 closing hole at the TPC at Sugarloaf. Johnson went for position with his first two shots, then knocked his third 25 feet over the hole. His birdie try dove hard to the left and now he needed to make his 3-foot par save to avoid a playoff and visit the winner's circle.
He ran the putt home, hugged his wife and choked back tears.
'It feels great,' said Johnson, who pocketed $810,000 for the win. 'I hope there's many more to come.'
Hensby nearly eagled the 72nd hole but settled for birdie and a round of 5-under 67. He came in at 12-under-par 276, while Scott Hend, who made his first cut on tour this week, took third place at minus-11 after a final-round 71.
Saturday's round featured ideal scoring conditions with little wind and warmer temperatures. On Sunday the winds were howling and at points, reached 30 miles per hour.
Johnson, who joined Todd Hamilton as the only tour rookies to win this season, began the round with a three-shot lead over Hend and Padraig Harrington, who played with Johnson in Sunday's final pairing at the TPC at Sugarloaf.
Johnson, despite a double bogey at the par-5 fourth, birdied three of his last four on the front side to make the turn with a three-shot lead over Hensby. Johnson reached the par-5 10th green in two and two-putted for birdie from 40 feet. Hensby missed a three-footer for par at the 12th and suddenly Johnson's margin was five.
Things fell apart quickly for Johnson.
At the par-3 11th, Johnson's approach came up 40 feet short of the flag. His birdie try was about five feet from getting to the hole and his par putt lipped out of the hole, giving him a bogey and dropping his lead to four.
Hensby sank a 3-footer for birdie at the reachable, par-4 13th, but Johnson dropped another shot to par at 12 and the edge was only two.
Johnson rebounded at 13 with a short birdie putt and Hensby made a mess of No. 15. His third went 30 feet long and he two-putted for a bogey to once again give Johnson a four-stroke lead over Hensby.
But Johnson would give some more strokes back to Hensby. Johnson hit a poor approach at the 14th that came up short of the putting surface. He chipped 12 feet behind the hole but the wind brought it back to 6 feet, but Johnson missed the putt to fall to 13 under par.
At the 15th, Johnson drove into the hay on the left side, then hit his second into a bunker on the left. His blast from the trap stayed on the fringe and his par-saving putt raced 3 feet past the hole.
Hensby was in the fairway at 18 and only two back. He looked disgusted after he hit his second from 220 yards out because he thought it was headed for the water. Instead, the ball stopped 40 feet right of the hole. Hensby needed an eagle to tie but the ball skirted over the right side of the cup. He tapped in for birdie and waited to see if Johnson would stumble on his way home.
Johnson played smart golf at 16 and 17, playing for the center of the greens. He two-putted for par at both holes, then took a 3-wood off the tee at No. 18. Johnson found the fairway and laid up with his second. His third landed 25 feet from the hole and briefly looked like it could roll into the water.
The ball stopped and Johnson two-putted for par and victory No. 1.
'It was a little scary,' said Johnson, last year's Nationwide Tour Player of the Year. 'I didn't hit that many bad shots. I putted very well all week. Fortunately it went my way.'
Hensby came close but still earned his best finish on the PGA Tour.
'Yesterday, I played really well. I shot 66 and missed one green and hit every fairway,' said Hensby. 'I felt pretty comfortable coming into today. The way I finished was great.'
Harrington had a wild round on Sunday. On his front nine, the Irishman collected an eagle, two birdies, two pars, two bogeys and two double bogeys for a 2-over 38. He came back with three birdies in a row from the 11th but bogeyed the 16th for a round of even-par 72. That was good for solo fourth at minus-10.
Peter Lonard shot a 71 on Sunday and took fifth, followed by two-time U.S. Open champion Lee Janzen (71) and 2003 BellSouth Classic winner Ben Crane (73). That duo was knotted at 7-under-par 281.
Luke Donald (69) and Stewart Cink (71) tied for ninth at minus-7 and Phil Mickelson posted a 1-under 71 to take 10th at 5-under-par 283. That was Mickelson's seventh top-10 in eight starts and with the $121,500 check for 10th, he moved to first on the tour's money list.