Texas Southern answered with with eight straight points to tie it at 50 and tied it again at 52 with 1:01 left in the game.
Aljau017e Kunc made a pair of free throws that gave the Cougars a 54-52 lead with 28 seconds left and Bonton made two more foul shots for Washington State to cap the scoring with 10 seconds to go.
Kunc added 11 points and Efe Abogidi in his college debut had nine points and eight rebounds for Washington State with nine points and six rebounds in the first half.
Texas A&M transfer John Walker III, Galen Alexander and Michael Weathers each scored 10 for Texas Southern.