Tennessee led by seven points at halftime, but MSU scored the first four points of the second half.
Mississippi State had a chance at the end of the game when Xavian Stapleton missed an open 3 from the corner with three seconds left.
The Bulldogs missed their fist eight attempts from beyond the 3-point arc before Lamar Peters connected with 1:12 left in the opening half. Play didn't stop after Weatherspoon's original fall, and Weatherspoon was kicked on the next possession.
The Bulldogs struggled offensively after the Weatherspoon injury but the Volunteers could not find separation.
Grant Williams grabbed 11 boards, the most he's had since the second game of the season against High Point.
The Bulldogs trailed by two at 58-56 after a trey by Peters. As a team, Mississippi State is scoring 74 points per game on 46.6% shooting from the field, 30.7% from behind the 3-point line and 68.5% from the foul line this season.
Tennessee held a 50-33 rebounding advantage.
Admiral Schofield added 13 points and SEC Player of the Year Grant Williams had 10 as Tennessee beat the Bulldogs (22-11) for the second time this season, having prevailed 76-54 on February 27 in Starkville, Miss. Tennessee is 8-3 ATS in their last 11 neutral site games and 4-1 ATS in their last 5 games against a team with a winning percentage above.600 while the under is 4-0 in their last 4 games overall.