Jon Severe scored 12 points for the 13th-seeded Rams (10-20), who snapped an eight-game losing streak and will take on fifth-seeded Dayton on Thursday. Travion Leonard added 10 points, while Ryan Canty brought down a career-high 19 rebounds.
Bryon Allen finished with 22 points for the 12th-seeded Patriots (11-20). Johnny Williams registered a double-double with 14 points and 10 rebounds, while Erik Copes cleared 11 boards.
Fordham made 45.5 percent of its field goal tries in the first period as it led 33-26 at the break. GMU shot just 33.3 percent from the field, including 1-of-7 from 3-point range.
The Rams connected on just 25 percent of their field goal attempts in the second half but went 21-of-31 from the free-throw line to hold on for the win. An Allen 3-pointer brought the Patriots within one with 15 seconds left. Fordham made three from the charity stripe down the stretch and Patrick Holloway missed a 3-pointer with one second left for GMU to seal the win for the Rams.
Fordham outscored GMU at the line, 21-11.