Tennessee (3-0) had a seven-point lead with 27.9 seconds left off a pair of foul shots by Cameron Tatum, but Jermaine Mallett hit a 3-pointer to make it 57-53 with 19.7 seconds left.
Missouri State's Adam Leonard answered another pair of Tatum free throws with a 3-point shot to cut the Vols' lead to 58-56 with 8.3 seconds left. Corey Copeland fouled Golden hard, sending him to the floor, but the Bears wouldn't score again after his free throws.
Tobias Harris led the Vols with 15 points, and Kyle Weems scored 18 for Missouri State.
"We weren't intimated by these guys," said Missouri State's Will Creekmore, who had 11 points. "They're very athletic and they're going to do big things this year."
Tennessee advances to face Virginia Commonwealth in the semifinals New York City on Nov. 24.
NO. 6 VILLANOVA 82, BOSTON UNIVERSITY 66
In Vallanova, Pa., Antonio Pena scored 17 points and Corey Fisher had 16 to lead Villanova past Boston University in the second round of the NIT Season Tip-Off.
The Wildcats (3-0) won their 40th consecutive game at The Pavilion, and advanced to the semifinals of the tournament next Wednesday night at Madison Square Garden in New York.
NO. 14 PURDUE 103, ALCORN STATE 48
In West Fafayette, Ind., E'Twaun Moore had 19 points, seven assists and six rebounds to help Purdue beat Alcorn State.
John Hart scored a career-high 16 points and made 4 of 6 3-pointers, Sandi Marcius had 12 points and eight rebounds and JaJuan Johnson added 12 points for the Boilermakers (2-0), who shot 52 percent from the field.
NO. 19 MEMPHIS 94, NORTHWESTERN STATE 79
In Memphis, Wesley Witherspoon scored 24 points and a career-high 12 rebounds, while Will Barton added 22 points, keying a second-half rally to help Memphis beat Northwestern State.
Witherspoon was 5 of 7 from the field and converted all but one of his 14 free throws as Memphis (3-0) survived a second-half burst by the Demons, who held the lead with just over 13 minutes left.