Johnathon Simmons scored 28 points and Houston went 10 for 10 from the free-throw line in the final 1:07 in a 73-71 victory over Southern Mississippi on Saturday night.
TaShawn Thomas had 11 points and 11 rebounds and Alandise Harris 11 points and seven rebounds for the Cougars (12-13, 4-8 Conference USA), who withstood a 3-point barrage by Neil Watson at the end.
Watson scored 27 points and made three shots from behind the arc in the last eight seconds for the Golden Eagles (22-5, 9-3), who remained tied atop the league standings thanks to Memphis' upset loss against UTEP on Saturday.
Jonathan Mills had 15 points and 14 rebounds for Southern Miss.
Mills layup with 1:35 remaining got the Eagles within 63-62, but Harris sank two shots from the line to begin Houston's string of free throws. Southern Miss missed four straight shots before Watson went on his late tear.
Joseph Young had 10 points for the Cougars.