Bryce Beall rushed for 105 yards and three touchdowns and Mark Hafner had 160 yards receiving for the Cougars, who are 3-0 in league play for the first time since 1990.
Keenum's 9-yard touchdown run brought the Cougars within 35-30 early in the fourth.
After an SMU field goal, Beall scored on a 1-yard run but Houston's two-point conversion attempt to tie the game failed. The Mustangs were forced to punt on their next possession, setting up the Cougars' game-winning drive.
Mitchell's desperation pass from near midfield on the final play of the game was intercepted.
The Mustangs last won a conference game on Nov. 18, 2006.
SMU jumped out to a 21-7 lead thanks to Mitchell's first TD run of the season and two scoring passes to Emmanuel Sanders, who set the SMU school record with 26 touchdown receptions.
The Cougars crept within 21-17 early in the third. Mitchell tossed a pair of touchdown passes to Robinson, including a 70-yarder on the final play of the third quarter to extend SMU's lead to 35-23.