Eastern Illinois scored on the game's second play from scrimmage on Shepard Little's 70-yard run, and Nick Bruno's 21-yard field goal gave the Panthers a 9-7 lead.
UT-Martin scored the next 30 points.
Favre's 13-yard TD to Rod Wright and 44-yarder to Ben Axline gave UT-Martin a 24-9 halftime lead.
Abou Toure paced UT-Martin (6-6, 5-3 Ohio Valley Conference) with 158 yards on 28 carries. Jarod Neal had a 45-yard touchdown run in the first quarter and Ladevin Fair had a 3-yard TD in the third quarter.
Andrew Manley was 26 of 50 for 290 yards and a score for Eastern Illinois (5-7, 5-3). Little finished with 137 yards on 13 carries and Adam Drake caught 11 balls for 146 yards and a 3-yard fourth quarter TD.