Jermaine Sanders added 11 points on 4 of 6 shooting, and Titus Rubleschipped in 7 points and grabbed 10 rebounds for the Bearcats (14-2, 3-0 American), which shot 37 percent from the field and 53 percent from the free throw line.
Brandon Morris led Houston (10-6, 2-1) with 17 points on 5 of 8 shooting from behind the arc. Jherrod Stiggers had 11 off the bench, and TaShawn Thomasadded 10 points and nine rebounds for Houston, which saw its three-game winning streak snapped.
Houston hit 7 of 10 from behind the arc in the second half, shooting 47 percent for the game, but hit 9 of 18 from the free throw line, including 3 of 9 in the second half.
Kilpatrick hit one of two free throws to up Cincinnati's lead to 59-54 with 51 seconds left. Stiggers was fouled shooting a 3-pointer with 33 seconds remaining, but hit just one of three free throws.
Justin Jacksonmissed both free throws for Cincinnati, and Thomas grabbed the rebound and his basket cut the lead to 59-57 with 12 seconds remaining.
Kevin Johnsonhit two free throws with 11 seconds to go to push the lead back to four.
After the Cougars had cut Cincinnati's lead to three with just under 10 minutes remaining, the Bearcats held Houston scoreless for the next 8:02, using an 8-0 run to push its lead to 58-47 on a Tony Caupain layup with 3:19 left.
Danrad Knowlesended the drought with a tip-in with 1:54 remaining, starting a 7-0 run, capped by a Stiggers 3-pointer with 53 seconds left to cut Houston's deficit to four.
Cincinnati opened the second half with the first three points to push its lead up to 19 points, but Houston responded with a 9-0 run to cut the lead to 43-33 on a Knowles jumper with 15:38 left in the game, prompting a Bearcats timeout.
After Cincinnati pushed the lead to 48-36 on a Sanders' 3-pointer with 12 minutes remaining, Houston answered again, this time with an 11-2 run to close within three on consecutive 3-pointers by Morris with 9:56 remaining.
Cincinnati used an 11-2 run over a five-minute stretch of the first half to open up a 26-13 lead with 7:24 left in the first half on two Titus Robles free throws.
Houston responded, closed the lead to 26-20, but the Bearcats ended the half on a 14-4 run to open up a 40-24 halftime advantage.