Trailing 58-56 with 23 seconds left in the second half, Towson's Mike Burwell hit two free throws to tie the game at 58.
DiNunno then missed a jumper that would have given Eastern Kentucky (3-0) the win, sending the game into overtime.
In the overtime period, Towson (1-2) jumped ahead 60-58 on Jerelle Benimon's tip in.
The teams exchanged baskets, until Muff's two free throws with 26 seconds left gave Eastern Kentucky the lead 69-67.
Marcus Dama's jumpshot on Towson's next possession tied the game at 69, but with just one second remaining, Benimon fouled Muff.
Muff hit two free throws to give Eastern Kentucky the 71-69 lead and the win.