The victory was the Patriots' first at Fordham's historic Rose Hill Gym and it sets up a first-round battle with Saint Joseph's Wednesday the A-10 tournament.
Greene shot 5 for 7 on 3-pointers.
Jordan Miller had 17 points for George Mason (16-15, 5-13). AJ Wilson added 10 rebounds. Josh Oduro had eight rebounds and four blocks.
Erten Gazi scored a career-high 22 points and had six rebounds for the Rams (8-22, 2-16). Antwon Portley added 11 points. Joel Soriano had 10 rebounds and three blocks.
For more AP college basketball coverage: https://apnews.com/Collegebasketball and http://twitter.com/AP-Top25
This was generated by Automated Insights, http://www.automatedinsights.com/ap, using data from STATS LLC, https://www.stats.com
Copyright 2020 by STATS LLC and Associated Press. Any commercial use or distribution without the express written consent of STATS LLC and Associated Press is strictly prohibited.