The Lobos have opened the Mountain West Conference season with four straight victories for the first time in school history. New Mexico's 17-2 record is its best at this stage of the season in 35 years.
The Rams trailed by 22 points during the middle stages of the second half, but rallied within three on a 3-pointer by Wes Eikmeier with 8 seconds to play.
Snell then hit his two free throws that clinched a fourth straight win for the Lobos. Chad Adams added 13 points for New Mexico.
Colorado State (15-4, 2-2) was led by 15 points and 14 rebounds from Colton Iverson. The Rams had won two in a row.