Stewart was 18-of-23 passing for 222 yards and threw all three of his scores to Brad Rozner, who finished with eight catches for 130 yards. Walter had 15 carries that included a 34-yard touchdown run.
Stewart threw TD passes from the 30 and 18, and his 34-yarder with 14 seconds left in the second quarter gave the Owls (1-9, 1-5 Conference USA) a 31-14 halftime lead.
Asher O'Hara threw for 338 yards and two touchdown passes and ran for another score for Middle Tennessee (3-7, 2-4).
The Blue Raiders fumbled the ball away on their first play from scrimmage but made it close with O'Hara's 7-yard touchdown run in the third quarter, and O'Hara's 20-yard touchdown pass to Jimmy Marshall with 3:22 remaining.
On the final drive, Rice converted on third-and-11 and chewed up more than three minutes of clock before punting into the Middle Tennessee end zone with 16 seconds remaining.
SEC suspends WR Jauan Jennings for first half of Vols' bowl game
Tennessee receiver Jauan Jennings has been suspended by the SEC for the first half of his team's upcoming bowl game after he stepped on an opposing Vanderbilt player in last week's regular-season finale.
Clay Helton will return for fifth season as USC coach in 2020
Clay Helton, who guided USC to an 8-4 record and is 34-17 (including 26-10 in the Pac-12) in his four full seasons as coach, will return in 2020, athletic director Mike Bohn said.
Mike Bobo reaches deal to step down at Colorado State
Mike Bobo, who went 28-35 in five seasons at Colorado State but just 7-17 over the past two years, has reached an agreement with the university to step down as coach.
Golic: People don't want to hear Dabo complaining
Mike Golic and Mike Golic Jr. discuss Dabo Swinney being outspoken to the media about Clemson's status in the College Football Playoff.
Ohio State's perfect regular season a blend of coaching, talent, focus
It took just the right mix of ingredients, starting with head coach Ryan Day, for Ohio State's Buckeyes to cook up a dominant 12-0 regular season.
Why coaches think LSU beats Georgia, and other conference title predictions
Scouting reports from every power-conference title game from the coaches who know these teams best.