Reynolds had a 3-yard score to cap the opening drive for Navy (9-4) and added a 1-yarder in the fourth quarter. Already with the NCAA record for touchdowns rushing by a quarterback, Reynolds upped his total to 31 to match Colorado State running back Kapri Bibbs, also a sophomore, for the national lead this season.
The only players with more rushing TDs in a season were Sanders (37) with Oklahoma State, and Wisconsin's Montee Ball (33).
Reynolds, playing 50 years after Hall of Fame quarterback and two-time Super Bowl champion Roger Staubach won the Heisman Trophy at Navy, still has two seasons left in college.
The Midshipmen ran 10 consecutive times on the game's opening drive, with Reynolds going 3 yards to put them ahead to stay.
"It's hard to simulate on a scout team what Navy does," Blue Raiders coach Rick Stockstill said.
Navy, which won for only the second time in its last seven bowl games, piled up 366 yards rushing and finished this season with five straight victories.
The Blue Raiders (8-5) were held to a season low in points. They had finished the regular season with a five-game winning streak, averaging nearly 43 points a game in that stretch since a 34-7 loss on Oct. 12 at North Texas, about 40 miles away from the TCU campus where the bowl was played.
"This was the first time we kept a team completely out of the end zone. It was huge to finish like this," senior linebacker Cody Peterson said.
"Last two games, our defense has played phenomenal," coach Ken Niumatalolo said. "Middle Tennessee has been moving the ball against a lot of people."
In its previous game, just more than two weeks earlier, Navy beat Army 34-7 in the snow and freezing temperatures in Philadelphia.
It was 32 degrees at kickoff on Monday, but with sunny and clear skies.
Reynolds lost two fumbles, matching his total during the regular season, Middle Tennessee failed to convert into points either of the miscues.