Danuel House had 19 points and Houston closed with a surge to beat No. 21 Memphis 77-68 on Thursday night.
TaShawn Thomas added 16 points and seven rebounds for the Cougars, who finished on a 14-5 run to win their second consecutive game. Jherrod Stiggers chipped in with 14 points and L.J. Rose had seven points, seven rebounds and 10 assists for Houston (14-14, 6-9 American Athletic Conference).
Houston shot 43 percent from the floor, including 8 of 21 on 3-pointers.
Michael Dixon Jr. scored 19 points and Shaq Goodwin had 16 points and 10 rebounds for Memphis (21-7, 10-5). Austin Nichols added 12 points.
The Tigers shot just under 47 percent but only 3 of 13 from 3-point range and committed 14 turnovers that led to 21 Houston points.
With the game tied at 63 with 3:53 remaining, Rose started the Cougars on their game-ending run with two free throws. House hit a 3-pointer before Dixon cut the lead to three with a layup with 1:33 remaining, but that was as close as Memphis got the rest of the way.
The Cougars hit eight of 10 free throws down the stretch in earning their second victory over a ranked opponent for the first time since the 2009-10 season.
Houston opened the second half with four straight points to extend its lead to 40-33 on two free throws by Rose with 18:57 left, but Memphis answered with a 15-4 run to grab a 50-46 lead on Dixon's 3-pointer with 12:47 remaining. Dixon had eight points in the spurt.
Houston answered with a 9-0 surge to take a 55-50 lead on a second straight 3-pointer by Stiggers with 11 minutes remaining, but the Tigers responded again with six consecutive points to grab a one-point lead with 9:46 left on Nick King's jumper.
In a back-and-forth first half, there were seven lead changes and five ties.
Memphis held four-point leads several times, the last time coming with 5:57 left in the first half on Goodwin's dunk, but Houston ended the half on an 11-4 spurt and scored the last six points to take a 36-33 lead at the break on House's four-point play.
Thomas came in needing five rebounds to become the seventh player in Houston history with more than 1,300 points and 800 rebounds in his career, joining Elvin Hayes, Dwight Davis, Greg Anderson, Rickie Winslow, Clyde Drexler and Hakeem Olajuwon.