Houston (4-1), coming off a loss to Texas-El Paso that knocked the Cougars from their first Top 25 ranking in 18 years, overcame a slow start.
The Bulldogs (2-4) intercepted Keenum twice -- one that Charles Mitchell returned 71 yards for a touchdown -- and sacked him once.
Still, Keenum completed 39 of 52 attempts for 434 yards.
The Cougars had 553 yards in total offense but were tied 17-17 going into the fourth quarter.
Keenum capped a 78-yard drive with a 3-yard scoring pass to Cleveland to put Houston ahead 24-17.
The Bulldogs came right back and appeared to tie the score when Anthony Dixon leapt into the end zone with 4:57 left. But a holding penalty nullified the TD and a fumble by Tyson Lee gave the ball back to Houston.
Less than a minute later, Keenum found Carrier from 18 yards out and the Cougars were up 31-17.
Dixon had 134 yards and two touchdowns on 21 carries. He had a 50-yard TD run in the second quarter, much of it draped with Houston defenders, to put Mississippi State up 14-7.
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Daryl Gross, who spent a decade as Syracuse's athletic director, will start as Division II Cal State-Los Angeles' AD in July.
Freshman DB Chad Clay didn't last long with the Georgia football team, as the Bulldogs dismissed him following a second arrest in the past four months.
Brenda Tracy, who allegedly was sexually assaulted by four men, including two Oregon State players, in 1998 spoke Wednesday to the Nebraska football team.
A man who claims he told Penn State football coach Joe Paterno in 1976 that he was sexually abused as a teen by Jerry Sandusky asked a judge Wednesday to protect his identity and limit questions.
FOX Sports' Bruce Feldman joins The Paul Finebaum Show to share his thoughts on the upcoming National Championship race.
Urban Meyer, Thad Matta and Ohio State athletic director Gene Smith were among the crowd at the parade for the Cleveland Cavliers on Wednesday.