Connor Cashaw grabbed 12 rebounds for the Owls (7-23, 4-14), who entered two games back of 12th-ranked UTEP (10-18, 5-11) and face fifth-ranked UTSA (17-13, 10-7) on Saturday.
Leading 36-29 at halftime, Rice opened the second half by scoring seven straight and led 50-40 on Tim Harrison's layup. Omega Harris scored seven straight and the Miners closed to 74-70 on his 3 with five seconds left, but got no closer. Adams hit two free throws and Harris' 3 at the buzzer missed.
Harris hit five 3s and scored 18 points, Isiah Osborne added 13 points, Paul Thomas had 12 and Trey Wade 10 for the Miners, who need a win Saturday at North Texas (17-13, 10-7) or a Rice loss at UTSA to make the tournament.
Len Chappell, who led Wake Forest to its only Final Four trip in 1962 and was an NBA All-Star with the Knicks, has died at 77.
Former UCLA basketball player Billy Knight, who was found dead on a Phoenix roadway early Sunday, was arrested in June and charged with six felonies, including two counts of molestation of a child.
Duke athletic director Kevin White will serve as the chairman of the NCAA tournament selection committee in 2020.
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