Nic Moore added 14 points as the Mustangs (19-5, 8-3 AAC) recorded their first such win since 1987 and remained unbeaten at home (13-0) with an eighth win in nine games overall.
Fans rushed the court after the victory -- the Mustangs' third triumph over a ranked opponent this season. They are likely to break into the Top-25 when new rankings are released Monday.
SMU hasn't made the NCAA Tournament since 1993.
The Bearcats (22-3, 11-1) had their 15-game winning streak snapped due in part to 17 turnovers.
Sean Kilpatrick led Cincinnati with 22 points.