Mason's 3-pointer with 6:09 remaining in the first half put the Purple Eagles (8-8, 4-1 Metro Atlantic Athletic Conference) ahead to stay, 21-19, and Green followed with two 3-pointers and a 2-point jumper for a 10-point lead, 29-19.
The Peacocks (6-9, 1-4) scored the game's first seven points before Niagara began to right itself.
Mason scored 19 of his points in the second half, making 7 of 9 shots, to keep the Purple Eagles comfortably in front.
Ameen Tanksley had nine points, seven rebounds and five steals for Niagara, which shares the MAAC lead.
Chris Prescott's three-point play with 1:10 remaining gave the Peacocks their only made free throw of the game in five attempts.