A sophomore transfer from Auburn, Douglas' 3-pointer with 5:18 left gave Florida State a 57-56 lead. He made another for a 64-59 lead with 2:56 left.
The difference was at the free throw line where Florida State made 22 of 30 while Wake Forest was just 6 of 12. Thornton, the ACC's leading scorer in conference play, was 11 of 13.
Florida State (15-5, 3-4) also got 11 points from Isaiah Swann, who came off the bench for the first time this season.
Kyle Visser finished with 17 points to lead Wake Forest, which also got 13 from L.D. Williams, one of its three freshmen starters. Another first year player, Ishmael Smith, had nine assists - two more than the Florida State team.
Florida State, which trailed by as many as eight early in the first half, caught up at 30-30 on Thornton's slam with an offensive rebound.
Wake Forest (9-11, 1-7) got a putback from the 6-11 Visser seconds later for a 32-30 lead at halftime.
It was almost a must-win for Florida State, which has already lost one ACC game at home and is again scrambling to qualify for a postseason NCAA bid.