Luke Hancock added 15 points, hitting eight of nine free throws, while Montrezl Harrell also had 15 for the Cardinals (19-4, 8-2 American).
The Cardinals shot just under 70 percent from the field in the first half, including 6 of 10 from behind the arc in building a 19-point halftime lead. Louisville finished the game shooting 56 percent.
TaShawn Thomas had 14 points and eight rebounds, and Jherrod Stiggers added 14 points to lead the Cougars (11-12, 3-7), who dropped their fifth straight and have lost seven of their last eight games. Danuel House had 11 for Houston.
Houston shot 46 percent from the field but committed 14 turnovers, leading to 24 points for the Cardinals.
Trailing 53-33 with 16 minutes remaining, Houston used an 18-7 run over the next 8 1-2 minutes to close within nine on Tione Womack's runner with 7:37 left. Stiggers had eight points in the run.
Louisville responded by pushing the lead back to 71-56 with 4:43 remaining on a Jones jumper. Houston would get no closer than 11 the rest of the way.
Louisville opened up a 15-point lead with an 18-3 run over a 6 1/2 minute stretch of the first half. Smith had six points on two three-pointers in the run that was capped by a Jones 3-pointer with 7:46 remaining in the half to make it 29-14. Houston was 0 for 3 from the field with five turnovers during Louisville's run.
The Cardinals lead expanded from there, growing to 40-19 on a Jones 3-point play with 4:13 to go in the first half.
Louisville led 45-26 at the half.
Houston honored longtime head coach and 2013 Naismith Memorial Basketball Hall of Fame inductee Guy V. Lewis in a pre-game ceremony. Former players including former NBA head coach Don Chaney and Hall of Famer Elvin Hayes were in attendance for the ceremony in which Lewis was presented with a proclamation that Wednesday was `Guy V. Lewis Day' in the city of Houston.