The Bobcats (12-13, 5-7 Southland) trailed 58-54 with 2:05 to play but closed the gap, thanks to a key 3-pointer by Jefferson. Brent Benson's 3-pointer with just 13 seconds left in regulation sent the game to OT.
Texas State scored the first six points of overtime, but the Colonels battled back. Anatoly Bose, who had 21 points, hit a 3-pointer for Nicholls, but White assured the win with his four straight free shots.
Brandon Bush scored 16 points for Texas State, and White had 12.
Ryan Bathie had 21 for Nicholls (15-10, 8-4), and Kellen Carter scored 10.