The Tigers (10-4, 1-1 Atlantic Coast Conference) came in as the country's top defense in points allowed, but it was the Seminoles (10-4, 1-1) who turned up the pressure to win their fifth straight game in the series.
Clemson's in-your-face defense seemed to rattle Florida State early as the Seminoles' didn't score the first 4 minutes. Then they went on a 13-2 run to gain a lead that they gradually increased to 16 points in the second half.
The Tigers got within 50-41 in the final 4 minutes, but Baron Bojanovsky broke free for a dunk. Clemson trailed by double digits the rest of the way.
K.J. McDaniels led Clemson with 14 points.
Florida State limited Clemson to 30 percent shooting and forced 18 turnovers, a season high for the Tigers.
Bookert made five of his six shots in the second half after going scoreless the first 20 minutes.
Florida State came into this one seeking its first win in ACC play this season and looking to lengthen its win streak over the Tigers. The Seminoles' five straight wins, including all three over Clemson last season, tied the longest mark by either school in the basketball rivalry.
The Seminoles took their time in starting at Littlejohn Colliseum, missing their first five shots and going scoreless for more than 4 minutes. Clemson, though, couldn't take advantage with only two points in the stretch, and that proved costly when Florida State finally got going.
Miller's 3-pointer and two jams by Thomas were part of 13-2 run Florida State used to take control.
Clemson, which entered leading Division I in scoring defense, had its share of stops in the opening half. The Tigers just couldn't overcome the taller Seminoles and were limited to 6-of-26 shooting the first 20 minutes.
Clemson went more than 6 minutes down the stretch without scoring until Adonis Filer was fouled on a drive to the basket with 2.8 seconds remaining. Filer made both shots to cut Florida State's lead to 21-16 at the break.
McDaniels, the Tigers' top scorer this winter, was just 2 of 6 from the field in the opening half for five points.
Thomas had eight first-half points for the Seminoles while Jarquez Smith had six.
Clemson's point total matched the second-lowest of Brad Brownell's four seasons as coach. The only fewer points came in a 68-40 loss to Duke a year ago. The Tigers take on the Blue Devils here Saturday.