McRae was held scoreless until the final three seconds of the first half, but he heated up in the second half and broke a 50-50 tie with just under a minute left. The Volunteers (10-8, 2-4 Southeastern Conference) led 54-50 before Trevor Releford hit a 3-pointer with 18.5 seconds remaining.
Alabama (12-7, 4-2) had one last chance to win the game after Trae Golden missed the front end of a one-and-one opportunity with 15.4 seconds left, but the Tide failed to capitalize.
Jarnell Stokes had 15 points and a career-high 18 rebounds for Tennessee. Releford scored 18, Trevor Lacey had 11 and Rodney Cooper added 10 for Alabama.
Check back with InsideTennessee.com shortly for more in-depth coverage of the victory.