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.
Gonzaga center Przemek Karnowski, who missed most of last season with a back injury, says he is returning for another year.
Wisconsin forward Nigel Hayes has withdrawn from the NBA draft and will return to the Badgers for his senior season.
Recruiting reporter Jeff Borzello has gotten grilled for his selections of underachieving and overachieving college basketball programs. He joins Phil Murphy to explain his rankings.