The Seminoles (10-2) advanced to Thursday's semifinal round, where they will meet Butler, despite shooting just 32.3 percent from the field against the Rainbow Warriors (7-3).
Chris Singleton grabbed 12 rebounds for Florida State, which scored 25 points off 23 Hawaii turnovers and held a 48-33 rebounding advantage.
Hawaii, which trailed 33-25 at halftime, cut the Seminoles' lead to 39-35 with 14:18 to play following Zane Johnson's 3-pointer. But White scored the next five points, spurring a 9-0 Florida State run to push the lead to 46-35.
Johnson led all scorers with 24 points. Bo Barnes had 17 points and Josten Thomas 12 for the Rainbow Warriors.