Eli Pepper's free throw with 10:29 left gave Lipscomb (2-3) a 54-49 lead but Miami score 11-straight points, including a 3-pointer by Mills, to open up a 6-point lead.
Brett Wishon hit a 3 to pull the Bisons within 1 with three minutes left. The teams traded 3-pointers before a jumper by Mills and two free throws by Eric Washington made it 67-62 with 21 seconds remaining.
Wishon hit another 3-pointer but Miami (2-1) made 3 of 4 free throws in the final 16 second to seal it.
Josh Williams, who led Lipscomb with 19 points, hit a 3-pointer as time expired. Wishon scored 16.
The Redhawks made 18 of 25 free throws while Lipscomb made 2 of 4.