It was the Vols' 10th all-time win at Coleman Coliseum (10-29) and just their fourth win in Tuscaloosa since 1981, spanning 22 games.
The Vols moved to 14-7 overall and 5-3 in the SEC with their seventh wire-to-wire victory this season.
Alabama dropped to 9-12 and 3-5 in the league. The loss was the worst home defeat for the Crimson Tide since falling by 26 to Clemson on Jan. 1, 2008, 87-61, and worst in an SEC game since 2003.
Josh Richardson added 12 points for Tennessee.
Stokes' monster night marked his 12th double-double this season and 30th in 71 career games.
The Vols shot 48 percent from the floor in the game including 71.4 in the second half (15-21). Tennessee made nine 3-pointers on the heels of an 11-of-20 performance in a win over Ole Miss on Wednesday. The Vols are 20-of-40 on 3-pointers in their last two games.
Tennessee committed just five turnovers. The third time this season the Vols had five miscues -- which is the fewest in any game since 1992.
Alabama was led by Trevor Releford and his 23 points.
Up by six at halftime, the Vols saw their lead cut to two early in the second half. But Tennessee responded with a 9-0 run finished off by a breakaway slam dunk by Thompson with 14:12 left in the game. That put the Vols up 47-36, their largest lead to that point.
Stokes stuffed home an emphatic slam dunk to increase the Vols' lead to a dozen at 53-41 midway through the second half. Richardson nailed a 3-pointer a minute later and the advantage moved to 13 at 56-43.
The Vols led by 17 on a McRae jumper with 5:30 left in the game at 64-47. The lead continued to balloon as McRae and Stokes poured in the points.
UT led by double-figures for the final 10:50 of the game.
Tennessee led 30-23 at halftime as McRae and Stokes each scored nine points. The Vols knocked down six 3-pointers in the first half.
McRae's third 3-pointer of the half put the Vols up by double-figures for the first time at 22-12 with 8:35 left in the half.
The Vols jumped out to a 9-0 lead thanks to a pair of game-opening 3-pointers by Thompson and Richardson. Alabama scored the next eight points to get back within one, but the Vols maintained a lead for the remainder of the half.
Tennessee returns to action on Wednesday as the Vols travel to in-state foe Vanderbilt for an 8 p.m., ET tip. That game airs on ESPN3 and can be heard on the Vol Network.
The Vols next home game is set for Saturday, Feb. 8 vs South Carolina at 3 p.m. That game airs on ESPNU.