Davis completed 14 of 26 passes to give the Golden Eagles (10-2) their first Conference USA Eastern Division title since 2006 and their first 10-win season since 1988.
Southern Mississippi will play at No. 8-ranked Houston in the conference championship game next Saturday.
The Tigers (2-10) have now won five games in the past three seasons combined.
Southern Miss running back Desmond Johnson rushed for 103 yards on 11 carries.
Tracy Lampley added 44 yards on seven carries and caught five passes for 116 yards, including a 49-yard touchdown from Davis on a flea-flicker. Southern Miss kicker Danny Hrapmann was 3-of-3 on field goal attempts and 5-of-5 on extra points.
The Golden Eagles defense forced three turnovers and returned a pair of interceptions for touchdowns.
Memphis (2-10) managed just 21 rushing yards on 23 attempts. The Tigers narrowly avoided a shutout with a late defensive score when Mitch Huelsing recovered a Southern Miss fumble in the end zone for a touchdown with 6:54 remaining.
Tigers quarterback Andy Summerlin completed 21 of his 45 attempts for 174 yards.