The defending ACC champion Seminoles (9-5, 1-0) led by 16 points on Michael Snaer's 3-pointer to start the second half, yet were ahead just 66-63 in the final minute with the ball in the Tigers' hands. But White stepped in front of Rod Hall's pass, was fouled and made both free throws to extend the lead.
Clemson (8-5, 0-1) got within 69-66 on Milton Jennings' 3-pointer with 4.5 seconds to go before Terrance Shannon iced the game for Florida State with two foul shots.
Snaer, the ACC's third-leading scorer coming in, scored all eight of his points in the second half for Florida State.
Devin Booker had 19 points and 11 rebounds to lead Clemson.
Terry Whisnant and Shannon had 11 points apiece for the Seminoles. Shannon also had a team-high eight rebounds.
Florida State's last win at Littlejohn Coliseum was in 2009 when it rallied from 19 down in the second half behind former star Toney Douglas for the victory. This time, it looked like Clemson might turn a similar trick on the Seminoles with a late rally.
Snaer's first bucket of the game, a 3-pointer just seven seconds into the second half, put the Seminoles comfortably in front 41-25. But the Tigers slowly reeled in their opponents. Freshman Jordan Roper hit a pair of 3-pointers as Clemson cut the lead to 60-57 with 4:24 left.
A tip-in by Shannon and a 3-pointer by Snaer built Florida State's lead back to 65-59 and Clemson couldn't get closer than 3 points the rest of the way.
K.J. McDaniels had 15 points, Roper 11 and Jennings 10 for the Tigers.
Florida State won the ACC regular-season title a year ago and was picked to finish fourth in league play this preseason. However, things didn't go as planned in nonconference play for the Seminoles. They lost early at South Alabama and have also fallen to Mercer to drop out of the national rankings. This past Wednesday, Florida State struggled at Auburn, losing 78-72, and faced another uphill fight at Littlejohn Coliseum, where it hadn't won since the 2008-09 season.
But the Seminoles came out fast and on target -- and all without leading scorer Snaer's help.
White and Ian Miller had two 3-pointers each in the first nine minutes as Florida State led 19-6. White's third 3 of the opening half increased the margin to 24-8 with 10:08 left before the break and the Seminoles' edge never slipped below double-digits the rest of the period.
Clemson couldn't find the basket early on, going 3 of 13 from the field and enduring a stretch of seven minutes without a field goal. McDaniel's basket with a minute left cut things to 36-25, but Shannon's inside bucket pushed Florida State's halftime lead to 38-25.
Snaer, who entered third in ACC scoring at 16 points a game, got one shot in the opening half and had zero points, content to watch his teammates connect from the outside. The Seminoles, eighth in ACC field goal percentage, were 15 of 30 for the half.
They slumped some after halftime, but still finished with 10 3-pointers.
Tigers fall short in comeback attempt
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