Tennessee (17-11, 8-7 Southeastern Conference) won for just the third time on the road this season. The Volunteers never trailed and led by as many as 14 in the first half, but the Bulldogs cut it to 67-63 with 2:14 remaining.
McRae hit two free throws to stop Mississippi State's run and preserve the win. The win keeps the Volunteers tied for fourth place in a crowded SEC race.
Jeronne Maymon added 10 points and 11 rebounds for the Volunteers.
Tennessee has been stuck in the middle of the SEC's widespread mediocrity this season. The Volunteers were one of seven teams tied for fourth place at the beginning of the week with a 7-7 league record.
Coach Cuonzo Martin juggled his lineup for Wednesday's game, starting guard Antonio Barton for the first time since Jan. 25. Barton didn't do much, but McRae and Stokes did, and it helped the Vols improve their road record to 3-7.
Tennessee never trailed, getting back-to-back buckets by Stokes in the first few minutes -- including one on an offensive rebound and dunk. The Volunteers were much bigger than the Bulldogs and used that bulk to their advantage in the first half, scoring 22 points in the paint on the way to a 35-24 halftime lead.
But Mississippi State fought back early in the second half, cutting the lead to 52-48 on a 3-pointer by Thomas with 10:55 remaining.
Tennessee regrouped quickly and McRae threw down two vicious dunks in a row to push the Volunteers lead back to 60-50. McRae's first dunk in the sequence was right through the heart of Mississippi State's defense while Bulldogs' coach Rick Ray shook his head in disgust.
Mississippi State hasn't won a game in more than a month and an encouraging 3-2 start to conference play in January is now a distant memory.
The game was played in a mostly empty Humphrey Coliseum and the fans who were in attendance couldn't muster much energy even when the Bulldogs made their run in the second half.
Mississippi State has been competitive lately, losing the last five games by 10 points or less.
Follow David Brandt on Twitter: www.twitter.com/davidbrandtAP