Moore was 4 of 8 from the 3-point line and 8 of 10 from the free-throw line in his ninth game with at least 20 points.
McMillan had 13 rebounds and 10 assists, Shemiye McLendon added 17 points and David Imes and Nathaniel Lester chipped in 10 each for the Pride (5-7).
Hofstra scored 20 points off 18 turnovers, and held Colgate without a fast-break point, as the Pride improved to 4-0 over the Raiders.
Hofstra led 44-41 with 16:12 remaining and went on a 10-2 run. Lester’s layup capped the spurt for a 54-43 lead with 12:37 to play.
McLendon scored 15 of his points in the second half.
Sterling Melville finished with 16 points and Nick Pascale had 13 points and 10 rebounds to lead Colgate (5-6).