Montes added a season-high 13 rebounds and Falzon 10 as each recorded a double-double. Phil Gaetano added 14 points and Evan Kelley 12 as the Pioneers (1-4) shot 47 percent from the field, forced 18 turnovers and out-rebounded the Rams 49-35.
Fordham (2-2) had the lead early and led by as many as seven points several times in the first half, but hit only 27 of 74 shots.
Montes hit a pair of free throws and fed Falzon for a jumper as the Pioneers went ahead for good 73-68 at 3:29.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.