Florida State's Bobby Bowden improved to 5-1 against his son Tommy, the Clemson head coach, by avenging a 26-10 loss to the Tigers last season.
Rix turned his right ankle with the Seminoles trailing 7-3 in the first quarter, but x-rays taken in the locker room were negative and he returned to the sideline before the end of the half.
He was 3-of-8 for 22 yards and Sexton 17-of-26. Chauncey Stovall caught seven passes for 96 yards.
This was the third-straight loss for Clemson (1-3, 1-2) after setbacks to Georgia Tech and Texas A&M.
Defensive back Justin Miller tied a Clemson record with two kickoff return touchdowns and had an NCAA single-game record 282 return yards.