Kohles fired a bogey-free nine-under par 63 at Grande Reserve Golf Club in Rio Grande to stand on 18-under 198 after 54 holes.
That lifted the American to a two-stroke edge over countrymen Jimmy Stanger and Brice Garnett and Germany's Matti Schmid as Kohles chased the first PGA title of his career.
World number 127 Kohles had his best PGA finish last November at the RSM Classic.
Kohles birdied all five par-5 holes, starting with the second and then again at the fifth, when he began a run of three consecutive birdies. Kohles birdied 12 and 14 before the par-5 15th and then closed with back-to-back birdies.
"Couldn't get much better," Kohles said. "I didn't really leave a whole lot out there. Was just feeling really good with the putter today.
"I just really tried to stay in the present, play my game. It was nice yesterday to finish off really strong and continue that today."
Schmid and Stanger seek their first PGA titles while Garnett won his only PGA crown in 2018 at Puntacana in the Dominican Republic.
American Joe Highsmith fired back-to-back 65s, completing his second round with a birdie and two pars Saturday morning, to seize a two-stroke lead after 36 holes, the round unable to finish before sunset Friday due to Thursday thunderstorms.
Highsmith fired a 71 in the third round to share fifth with fellow American Erik Barnes on 201.
The tournament is played opposite this week's Arnold Palmer Invitational at Bay Hill, one of the PGA Tour's signature events designed to showcase the game's top talent.