Jarreau had 10 points in the second half, and Davis finished 12 of 13 from the free-throw line as the Cougars (21-1, 8-1 American Athletic Conference) shot 43 percent from the field. Breaon Brady had 13 points and six rebounds.
Houston has won six straight since a 73-69 loss at Temple on Jan. 9 and has won 31 straight home games.
Quinton Rose scored 26 points and Alani Moore II added nine points for the Owls (15-6, 5-3), who have lost three of its last four. Temple shot 34 percent from the field.
After Houston pushed the lead to 67-57 on Davis' two free throws with two minutes left, Temple scored five straight points to close within five on Nate Pierre-Louis' two free throws with 1:13 left. Davis hit six straight free throws in the final minute.
After Temple cut Houston's lead to 50-48 on J.P. Moorman II's 3-pointer with 9 minutes remaining, Houston responded with seven straight points to open up a nine-point lead on Jarreau's three-point play a minute later.
The Cougars scored eight straight points to build a 35-27 lead on Galen Robinson Jr.'s free throw with 1 minutes left in the first half. Davis scored four of his nine first-half points on the run, and Houston led 35-29 at the half.
BIG PICTURE
Houston: Armoni Brooks, the Cougars' leading scorer at 14.8 points per game, had a quiet night due to foul trouble. Brooks sat most of the first half with two fouls and finished with three points. Houston held a 34-24 advantage in points in the paint.
UP NEXT
Houston: Travels to Central Florida on Feb. 7.