Overton, looking for his first PGA Tour win, finished 54 holes at 18-under 192, leading D.A. Points (61) by three shots at minus-15 and third-place Boo Weekley (67) by five at minus-13.
The main attraction Saturday at The Old White Course, however, came as both Points and J.B. Holmes flirted with 59s.
Points needed just one more birdie to shoot a 59 after going 10-under through his first 16 holes. But he three-putted for bogey at the 17th and made a routine par at the 18th to fall two strokes short.
Holmes, meanwhile, finished with a 60 after missing a 4-foot birdie putt at No. 11 and a 10-footer for eagle at No. 17.
Holmes ended up sharing fourth place with Jonathan Byrd (64), Brendon de Jonge (65) and Jimmy Walker (67).