J.J. Avila scored 15 points with 11 rebounds and Gian Clavell added 10 for the Rams (20-4, 7-4 Mountain West).
Rashad Vaughn's layup sparked a 21-4 run and the Runnin' Rebels seemed headed for a blowout with a 36-18 lead, but the Rams rallied behind Bejarano's nine points to trail 41-39 at halftime.
The Rams led 43-41 early in the second half on a jumper by Avila, but UNLV's Jelan Kendrick tied it at 64 with a layup. The lead traded hands four times until Bejarano hit back-to-back 3s for an 80-77 CSU lead with 1:57 left. Patrick McCaw's 3 pulled UNLV within 83-82, but Jordan Cornish's shot with three seconds left missed.
Vaughn scored 30, including six 3s, for UNLV (13-10, 4-6) and Wood and McCaw scored 16 apiece, with Wood grabbing 11 rebounds.