The Midshipmen (8-20, 2-10) led 27-22 at halftime but made just one field goal in the first 13:24 of the second half.
Mitch Rolls and Moore hit 3-pointers and Murphy Burnatowski a layup in the first 2 minutes to give Colgate (11-18, 5-7) a 30-27 lead it never relinquished.
By the time Worth Smith hit a 3-pointer to end a Navy field goal drought of 11:08, the Raiders led by 15 points, 47-32.
Navy shot 6 for 24 in the second half.
Moore and Clayton Graham, who finished with 10 points, led a strong performance by Colgate’s bench, which outscored Navy’s reserves 37-4.
The Raiders also dominated on the boards, with Luke Roh’s 12 rebounds helping build a 46-28 advantage.
Tilman Dunbar led the Midshipmen with 13 points.