New Mexico (14-4, 5-1 Mountain West) never trailed and led by as much as 32-15 in the first half.
At one point, Greenwood scored 11 of the Lobos' 15 points sandwiched around halftime, helping them to a 49-34 lead 3 minutes into the second half.
Derrick Marks scored 20 for the Broncos (13-6, 3-3), including 15 in the second half when they began to get back in the game. Boise State's Ryan Watkins also contributed to the comeback, controlling the boards and scoring nine of his 15 points after the break to help the Broncos pull within 74-68 with 3:24 left.
But the Lobos got a 3-pointer from Kendall Williams, who finished with 18 to extend the lead again.