Dasher completed 15 of 25 for 162 yards and ran for 201 yards to give him 1,175 on the season.
Middle Tennessee (10-3), playing in the second bowl game in school history, concluded its best campaign since joining the Football Bowl Subdivision in 1999.
Southern Miss (7-6) was playing in its eighth straight bowl game, the 12th in the last 13 seasons. The Golden Eagles had won their three previous New Orleans Bowls.
Southern Miss running back Damion Fletcher ran for 78 yards and became the ninth player in major college football to reach 1,000 in all four seasons.