Keoke Cotner carded a 6-under 65 to take second place at 11-under-par 273, while former PGA Tour winner Dicky Pride managed a 70 to share third place with Tom Scherrer at 10-under-par 274.
Johnson, who established a course-record for StoneWater Golf Club with his 62 on Saturday, stumbled out of the gate with a bogey on the first. He got that stroke back as he rolled in a 20-foot birdie putt on the third.
The 33-year-old dropped his second shot 4 feet from the cup at the fifth and sank that birdie putt. Johnson made it two straight as he made a 12-foot birdie putt on the sixth.
Johnson, who entered the final round tied with Australian Matthew Jones, made a 15-foot birdie putt on 10 to get to 13 under. He tripped to a bogey at the 12, but birdied 13 from 20 feet out.
After a pair of pars, Johnson dropped a sand wedge within 5 feet at the 16th to set up birdie and ran in a 15-foot birdie try at 17 to get to 15 under. However, Johnson closed with a three-putt bogey at the last.
'I don't think it has sunk in yet,' said Johnson, who earned $81,000 for the win. 'Even on 17 when I looked up and saw my name on the board, I thought 'does that say four shots?' Early on I was really, really nervous.'
Johnson, who was 150th on the money list entering the week, flew all the way up to 41st on that list.
'I'm sitting at 150, $1,000 gets you nowhere,' Johnson said. 'I was at my wits end. I was hitting it terrible at the beginning of the week. I think today the putt on No. 3 woke me up. It is great to hit the shots and make the putts you need to.'
Cotner birdied the first, then ran off three straight birdies from the fourth to get to 9 under. He ran in a 10-footer for birdie at eight.
The 34-year-old missed a par putt on the 11th, but got that stroke back when he drained a 25-footer for birdie on the 12th. Cotner posted his final birdie at the 15th from 6 feet out.
'I drove the ball good and hit my irons well,' Cotner said. 'Credit to Andrew, it's tough to come back from a round like he had on Saturday. Everything seems to be in order now. I'll take this for the next eight weeks.'
David Morland IV posted a three-under 68 to finish in fifth place at 9-under-par 275. Rick Price (68), Jones (73) and Ben Bates (68) were one stroke further back at minus-8.