Tinnon had 24 points and 10 rebounds and Pitts had 19 points and 11 assists in the third straight win for the Thundering Herd (8-2).
Pitts missed two free throws with 5 seconds to go. However, Kerron Johnson, whose free throws made it 87-86, missed a potential game-winning layup for the Bruins with 1 second left.
Adam Barnes' free throws capped a 5-0 run by Belmont to put the Bruins up 84-83 with 1:55 left. Pitts' layup gave Marshall an 85-83 lead with 32 seconds to go.
Tinnon finished the scoring for Marshall with two free throws with 11 seconds left.
DeAndre Kane added 29 points for Marshall, which stifled Belmont from beyond the arc. The Bruins (7-5), averaging 9.2 3-pointers a game, were just 7 of 22.
Johnson finished with 18 points.