Toney Douglas led the way with 23 points as the 'Noles inched closer to their first NCAA tournament bid in 11 years.
Meanwhile the Tigers are now fighting for a first-round bye in the ACC Tournament after looking to be easily ranked among the top four teams in the ACC just one week ago.
"We've got to get back home and take care of business," Purnell said. "We got back in it, but it's like being on a high wire."
The Seminoles led 39-27 at halftime and opened their largest advantage at 51-33 early in the second half, but Clemson closed to within 63-60 on five points by Raymond Sykes in a span of just 12 seconds.
Douglas hit six straight free throws in the final 2:48, including four in a row in the final 50 seconds that stopped Clemson's comeback.
Booker, the Tigers leading scorer on the season, went scoreless until there was just 1:50 left in the half when he hit a close-range scoop shot.
Florida State, which rallied from a 19-point deficit with under 15 minutes left in the game three weeks ago at Clemson to win 65-61, clinched just its second winning record in ACC play in the past 16 years.
The Seminoles capitalized on a 25-7 run to build a 14-point lead in the first half.
Clemson (22-6, 8-6) was led by K.C. Rivers 17 points. Trevor Booker was held to eight points, but pulled down a game-best 13 rebounds.
Derwin Kitchen and freshman Chris Singleton each had 10 points for the Seminoles, who swept Clemson for the first time since the 2000-2001 season.
Terrence Oglesby added 12 points for Clemson on 4-of-10 shooting from 3-point distance while Sykes finished with 10 points and four blocked shots.
Florida State visits Duke on Tuesday and closes its regular season at home next Sunday against Virginia Tech.
Clemson hosts Virginia on Tuesday and finishes next Sunday at Wake Forest.
Clemson rally falls short
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