Houston (4-3, 3-0 Conference USA) trailed 35-23 heading into the fourth quarter before Keenum, who surpassed 300 yards passing for the eighth straight game, engineered the comeback.
Trailing 38-36, the Cougars got the ball at their own 15 with 1:58 left.
Keenum, who completed 28 of 36 passes for 404 yards, was 5-of-6 on an eight-play drive. He capped it with his TD pass to Carrier, who made a nice over-the-shoulder catch in the end zone.
SMU (1-7, 0-5) has lost 14 straight conference games and 17 in a row to FBS teams. The Mustangs' only win this season was against FCS school Texas State.
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.
Oklahoma running back Samaje Perine is the winner of the Capital One Cup Impact Performance of the Week.
Texas A&M offensive coordinator Jake Spavital breaks down film of key offensive plays from Texas A&M vs. Vanderbilt.
The Florida State University official once in charge of the office that counsels campus rape victims told lawyers suing the school that football players receive special treatment, and that most o
Amid mass speculation, Les Miles said he has "no idea" where he stands as LSU's coach and hasn't spoken to athletic director Joe Alleva, but he expects to at their annual postseason meeting.
Welcome to the Thanksgiving edition of the Pac-12 mailbag, which includes playoff talk and analysis of Rich Rodriguez's future.
After months of cheering for your team to win, its time to extend that goodwill to others. Heather Dinich breaks down who you need to cheer for if you want your team to make it in to the College Football Playoff.