Wes Eikmeier had 19 points for the Rams (5-2), who have won three straight, and Green finished with nine.
Spencer Dinwiddie matched a career-high with 16 to lead Colorado (4-3). Austin Dufault had 13 and Nate Tomlinson, who missed a 3-pointer as time expired, added 11.
The Buffaloes were 13 for 29 from the free-throw line.
Tomlinson gave Colorado a 64-63 lead with a shot in the paint, but Green beat the Colorado defense down the court for the game-winning layup.
Colorado State’s lead reached double digits, 37-27, early in the second half when Eikmeier hit two free throws after a technical on Tomlinson, then added a 3-pointer on the same possession. Colorado closed the gap to 48-45 on Tomlinson’s 3-pointer with 12:18 left.