Louisiana Tech's Raheem Appleby missed a pair of 3-point attempts in the final 7 seconds that could have tied the game.
Thomas has scored 20 or more points in all three of FSU's NIT wins. He also had nine rebounds.
White finished with 20 points and eight rebounds.
FSU (22-13) will play Minnesota in the NIT semifinals on Tuesday night at Madison Square Garden in New York. The Seminoles have advanced to the NIT semis for the first time since 1997.
Kenneth Smith had 16 points and 14 rebounds, and Cordarius Johnson added 11 points for Louisiana Tech (29-8).