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.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.