Kuchar's birdie putt at the par-5 finishing hole moved him to 14-under-par 199, snapping what was a four-way tie atop the leaderboard.
Kevin Johnson, Nick Malinowski and Stephen Marino all posted 4-under 67s to move from a tie for seventh place overnight into a tie for second place at 13-under-par 200.
Brad Ott shot a 3-under 68 and is alone in fifth place at minus-12, one shot ahead of seven players who are tied for sixth.
Gavin Coles, who shared the second-round lead with Kuchar, carded a 2-over 73 and tumbled into a tie for 13th place at 10 under -- one day after setting a course record with his 10-under 61 on Friday.
Coles was done in Saturday by a triple-bogey at the par-4 seventh and three bogeys over his final 10 holes at Crestview Country Club's North Course.
Meanwhile, Kuchar, 28, treaded water until late in his round. He birdied the par-5 second, then gave that shot back with a bogey at the par-4 sixth.
After going birdie-bogey at the ninth and 10th, Kuchar was even-par for his round. He parred five consecutive holes after that before birdieing two of his last three.
At the par-4 16th, he knocked a wedge within 12 feet to set up his third birdie of the day. Then, at the 18th, a chip to three feet set up his go-ahead birdie.
Birdies were harder to come by Saturday than they were in the first two rounds when a lift, clean and place rule was in effect on a soggy course.
'It's amazing what some sunshine can do to a course,' said Kuchar. 'It played awfully difficult today.
'If you would have said last night that 14-under would be leading, I would have said no way.'
Kuchar, winner of the 2002 Honda Classic on the PGA TOUR, picked up his first Nationwide Tour victory in May at the Henrico County Open. He has never held the 54-hole lead before on either tour.
'The more times you can get in that winner's circle the more prepared you are,' Kuchar said.
Jaco Van Zyl carded the round of the day with a 6-under 65. He shares sixth place with Scott Gardiner (66), Craig Lile (66), Patrick Damron (68), Michael Sim (68), David Hearn (69) and Hunter Haas (71) at 11 under.