After a jumper by Lucas Jones put Eastern Illinois up 2-0, Tennessee State went on a 15-3 run and never again trailed.
The Tigers led by as many as 17 in the first half, but Eastern Illinois (4-11, 1-2) slowly chipped away. The Panthers tied it 42-all midway through the second half, and used a 10-3 run - including 3s by Demetrius McReynolds and Cornell Johnston - to make it 60-59 with 39 seconds to play.
McCall sandwiched two pairs of free throws around a layup by Eastern Illinois' Trae Anderson to give Tennessee State a 64-61 advantage with seven seconds left.
Anderson, who led the Panthers with 20 points, missed a potentially tying 3-pointer a few seconds later.