Johnson birdied three consecutive holes from the 14th, bogeyed the 17th and then closed with a par for his fourth win and first since the 2000 Permian Basin Open. He finished four rounds at 18-under-par 266.
'It's been a long while,' Johnson said. 'I think I performed better than I thought I would.'
Kuchar, who led Johnson and two others by one shot overnight, ended one stroke back at 17-under-par 267. Looking for his second win in three months, he finished birdie-bogey-birdie and shot a 3-under 68 Sunday.
'It was fun playing with K.J. The two of us were playing good golf,' said Kuchar. 'To have a chance to win was a lot of fun.'
Johnson drained short birdie putts at Nos. 2 and 9 and make the turn at 15 under, one shot behind Kuchar. But while Johnson went on to collect a birdie at 11 and three straight from the 14th, Kuchar went just 1 under on the same holes.
With Kuchar now two shots back, both players bogeyed the 17th before Kuchar birdied 18 to finish one behind. Johnson made his par at the par-5 18th from a fairway bunker, two-putting from 25 feet to avoid a playoff.
'We both grinded it right up until the end,' Johnson said.
Johnson, 39, was a member of the PGA TOUR in 2001, collecting his best-ever finish on that circuit with an 11th place tie at the Bob Hope Classic.
Last year, he finished tied for 65th at the Honda Classic on the PGA TOUR and no better than fifth in 17 starts on the Nationwide Tour. Until Sunday, this season had been no different: Johnson had made just three cuts in 13 previous starts on the 2005 Nationwide Tour schedule.
Four consecutive sub-69 rounds this week took care of the drought.
'It beats up on you not performing like you ought to,' said Johnson, who is now tied for the third most wins in Nationwide Tour history alongside, among others, Olin Browne, Joe Ogilvie and U.S. Ryder Cup captain Tom Lehman.
'I'm 39 years old. I don't want to go out there finding a new job, and this is definitely a kick-starter.'
Australia's Scott Gardiner and South African Craig Lile tied for third place at 15-under after both carded 4-under 67s in their final round.
Erik Compton and Canadian David Hearn were one stroke further back in fifth place. Compton shot a 67 on Sunday and Hearn had a 68.