George Beamon added 10 points for the Jaspers (2-3).
Ryan Canty led Fordham (1-5) with 18 points and Branden Frazier had 16.
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.