Brooks Ybarra made four free throws in the last 17 seconds for the Bobcats (6-2).
Jonathon Simmons had 26 points on 8-for-11 shooting and TaShawn Thomas had 11 points and 13 rebounds for Houston (4-4). Alandise Harris and J.J. Thompson also had 11 points for the Cougars, who trailed 50-34 at halftime and by 23 points three minutes into the second half, but rallied to get within 74-72 with just over a minute to play.
Davis made one of two free throws with 6 seconds left, putting Texas State’s lead at three points, but Thompson missed a 3-pointer that would have tied it. Texas State was 10 for 21 at the free-throw line while Houston was 22 for 31.