Bernard James added 13 points and 11 rebounds for his seventh double-double of the season while Xavier Gibson had 13 points for Florida State, which had five players finish in double figures.
The Seminoles (21-9, 12-4) finished third in the Atlantic Coast Conference behind No. 6 North Carolina and No. 4 Duke and have a first-round bye in the league tournament that begins Thursday.
K.J. McDaniels and Andre Young scored 16 points each for Clemson (16-14, 8-8), which pulled within 75-72 with 30 seconds left on two free throws by McDaniels, but Florida State made five of six free throws over the final 28 seconds to hang on.
Clemson will be the 7th seed at the ACC Tournament. The Tigers will face Virginia Tech at 7 p.m. on Thursday in Atlanta. Winner of that game will play Duke.