Houston (14-7, 3-5 Conference USA) forced the overtime after trailing by 17 points at halftime. The Cougars outscored the Mustangs (12-11, 2-6) 53-26 in the second half.
Joseph Young led the way for Houston with 17 points. Stiggers had 16 off the bench, including 4 of 7 from 3-point range. TaShawn Thomas scored 15 points, J.J. Thomson scored 13 and Danuel House scored 10.
Nick Russell scored 22 points and Jalen Jones added 21. Ryan Manuel scored 15 points and handed out a career-high 10 assists.