George Beamon added 10 points for the Jaspers (2-3).
Canty made a layup with 2:56 left to bring the Rams to within 55-54, but the Jaspers went on an eight-point run to make it 63-54 with 22 seconds remaining. Rhamel Brown made a layup and a free throw, and Alvarado made three free throws, Beamon two and Kates two to close out the scoring for Manhattan.
The Rams turned the ball over three times down the stretch, and their only lead was at 3-2.
Manhattan shot 45 percent from the field (18 of 40) to Fordham's 36.5 percent (20 of 55), and the Jaspers outscored the Rams 26-15 from the foul line.
Mike Brey is looking at former Notre Dame players to fill two assistant jobs that have opened up with the departures of Martin Ingelsby and Anthony Solomon.
Purdue's 2016-17 prospects got a jolt Wednesday when forward Caleb Swanigan announced he will return for his sophomore season.
Clemson's Jaron Blossomgame says he is withdrawing from the NBA draft and returning to school for a final season.