Wichita State pushed 14th-ranked Houston to two overtimes but couldn't pull out a win.
J'Wan Roberts' dunk with 1.2 seconds left gave the visiting Cougars a 76-74 victory on Sunday afternoon in front of a season-high 9,070 fans at Charles Koch Arena.
Craig Porter Jr. scored 17 points to lead the Shockers (13-11, 4-8 American), including step-back three-pointer that knotted the game at 74 with 5.4 seconds remaining.
Josh Carlton tallied 23 points (12 of them in OT) and 11 rebounds for Houston (22-4, 11-2), which maintained its one-game lead over second-place SMU in the American Athletic Conference standings.