Coleman scored 11 points and grabbed 10 boards for the Jaguars (16-11, 9-7 Sun Belt Conference), who won their third straight game and five of the last six. Ronald Douglas and Domonic Tilford also added 11 points apiece.
After relinquishing a 26-23 halftime lead, the Blue Raiders pulled within 57-52 on Calvin O'Neil's jumper with 1:23 left. But Garner hit five free throws in the game's final 39 seconds to seal the win for the Jaguars.
South Alabama hit 28 of 42 free throws, while MTSU went just 5-for-12 from the line.