Giddy Potts chipped in 11 points for Middle Tennessee (12-5, 4-1 Conference USA), who has won four straight.
The Monarchs led 29-24 early in the second half and had no more than a four-point lead until Reggie Upshaw made a layup to give the Blue Raiders a 47-46 lead with 7:50 remaining. A 15-10 spurt stretched it to 62-56 with 29 seconds to go.
Freeman made two free throws and a 3-pointer to pull the Monarchs to 63-61 with 10 seconds left. Simpson split a pair of free throws, Talley missed a 3-point attempt and Potts grabbed the board to end it.