The Volunteers remained unbeaten in three games this season, but had to sweat out the victory after briefly falling behind by three points early in the second half.
Cameron Tatum hit 1-of-2 foul shots for Tennessee with 16 seconds to go to give the Volunteers a five-point advantage, but Adam Leonard hit a 3-pointer for the Bears with 11 seconds to play.
Golden's free throws made it a two-possession game and Missouri State could not score again. The Bears slipped to 2-1.
Tobias Harris scored 15 points to lead Tennessee, which shot 39 percent from the field and missed 10-of-28 free throws. Tatum and Scotty Hopson both had 12.
Missouri State was paced by with Kyle Weems with 18. The Bears rallied to throw a scare into Tennessee after trailing by as many as 11 late in the first half.