Bristol had 11 points and 16 rebounds for the Rams (4-4), who moved to .500 for the first time since Jan. 19, 2008.
The Jaspers (2-7) lost their seventh straight.
Trailing 23-17, Fordham used a 9-0 run to lead 26-23 with 6:21 left in the first half.
Manhattan tied the game, but a 7-0 spurt, capped by a Bristol dunk, gave the Rams the lead for good at 35-28.
After Kidani Brutus made a 3-pointer to pull the Jaspers within eight at 48-40, Fordham outscored Manhattan 10-2.