McCall scored nine of the Tigers' final 13 points in the last five minutes.
After McCall and Murray State's Bryce Jones each traded a pair of free throws, McCall countered with a 3-point play to pull Tennessee State (14-4, 5-0 Ohio Valley) within 67-65 with four minutes left. Wayne Martin made a pair of free throws to tie it.
Marcus Roper hit a layup, and McCall made two more free throws to put the Tigers up 71-67 with 1:12 left.
But Murray State's Jeffery Moss hit a layup and Jones converted two free throws to tie it at 71 with 23 seconds left.
Keron Deshields finished with 15 points and Wayne Martin added 12 for the Tigers.
Jones led Murray State with 18 points and was 10 for 10 from the free-throw line.