The Colonials (4-7) jumped ahead to an early 24-10 lead sparked by a trio of 3-pointers from Anderson, but Duquesne closed the first half on a 19-7 run to make the score 31-29 at the break.
Anderson hit his fourth and fifth 3-pointers of the game to fuel an 8-2 run, giving Robert Morris a 10-point lead with 3:24 remaining.
McKoy netted two free throws, but Anderson sank one of two from the stripe to cut the rally short.
Myers-Pate and Charles Oliver each scored 10 points for the Colonials.
McKoy led Duquesne with 16 points on 5-of-6 shooting and 10 rebounds.