The Golden Gophers (22-14) earned a trip to New York for next Tuesday's semifinals, in which they will take on Washington. Minnesota lost seven of its last nine games during the close of the regular season and the Big Ten Tournament prior to running off three victories thus far in the NIT.
Middle Tennessee closed within three points on two foul shots by Marcos Knight with 33 seconds to play, but Hollins was perfect from the line the rest of the way to fight off the Blue Raiders.
Both Hollins and Rodney Williams had 24 points for Minnesota.
Middle Tennessee (27-7), which won the regular-season title in the Sun Belt Conference, only to lose in the quarterfinals of the league tournament, had defeated Marshall and Tennessee to get to the NIT quarters.
Knight led the Blue Raiders with 19 points.