The Minutemen (11-4, 1-1), whose 70-62 loss Thursday at Saint Louis snapped their seven-game winning streak, took a double-digit lead with 7:21 left in the first half and led by 14 in the second.
But the Rams chipped away, getting within two points with 2 minutes left and again with 1:04 remaining. Freddie Riley hit a 3-pointer from the corner with 34 seconds to go and Massachusetts hit 5 of 6 free throws in the final 26 seconds to hold on.
Terrell Vinson added 19 points for the Minutemen, Trey Davis a career-high 12 and Riley 11. Cady Lalanne had 11 rebounds.
Branden Frazier had 21 points for Fordham (5-12, 1-1) and Chris Gaston added 20 points and 13 rebounds. Ryan Canty grabbed 13 boards as the Rams dominated the glass 55 -42.