Deon Jones had 11 points and 11 rebounds for the Hawks (9-3), who have won eight times on the road this season - the most in the nation.
Robert Hatter had 27 points and JoJo Fallas added a career-high 17 for the Big Red (5-6), which lost for the first time in five home games.
Cornell got off to a quick start and lead by 10 on Hatter's 3-pointer at the 13:42 mark. Jones had a jumper and a 3-point play in a surge that pulled Monmouth within one and the Hawks, with Robinson scoring twice, closed the half on an 8-0 run to lead 37-34.
Austin Tilghman had a 3-point play with 6:30 to play to start a 6-0 run to put Monmouth up 66-58 and the Hawks made 6 of 7 free throws in the last 1:21.