Mann hit four 3-pointers and 7-of-8 from the free throw line for the Bruins (26-9), who took down Green Bay in the opening round. Drew Windler and Craig Bradshaw contributed 18 and 17 points, respectively.
Belmont will take on the winner of Sunday's tilt between Clemson and Illinois.
Karvel Anderson's 23 points paced Robert Morris (22-14), which has won a game in this tournament in consecutive seasons. The Colonials shocked then No. 1 seed Kentucky in last year's NIT and upset No. 1 St. John's earlier this week.
RMU scored on its first four possessions, jumping out to an 11-5 lead two minutes in. Blake Jenkins scored six points, including a pair of dunks, during a 10-0 Belmont flurry later in the frame.
The Colonials went back in front, 25-19, before Mann went on a personal 8-0 run to ignite the Bruins' attack. Belmont eventually turned the run into a 17-0 surge, which Bradshaw capped with his three-point play late in the period.
Belmont owned a 44-35 halftime lead and led by at least six points the rest of the way.