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.
Ben Simmons explains what he is focusing on ahead of the start of his NBA career.
After John Calipari's comments about the Louisville scandal, Rick Pitino says that Calipari should not be worried about other programs and to keep quiet unless he is praising another institution.
College basketball coaches across the country will hit the recruiting trail hard in July to target the Class of 2017's top prospects. Which players are the nation's top programs targeting?