The Blue Raiders (4-4) were trailing late in regulation when Edward Simpson Jr. and Jaqawn Raymond each hit 3-pointers in the final two minutes to force overtime.
Ken Williams hit a 3-pointer in overtime for South Alabama (2-4), but Rozier responded with a split pair of free throws, then took the lead for good with a layup. Raymond hit two free throws for a 68-64 lead with 13 seconds left.
Taishaun Johnson drilled a 3 and was fouled, but couldn't convert the four-point play. Reggie Upshaw Jr. missed two free throws, and Johnson's half-court heave was off as time expired.
Raymond finished with 11 points and Upshaw had 10 for Middle Tennessee.
Abdul Lewis led the Jaguars with 17 points and 12 rebounds.