The Rams overcame an 11-point halftime deficit to take the lead in the final 4 minutes, but eventually missed out on a chance to move into a tie with New Mexico for the lead in the Mountain West Conference.
Bryce Dejean-Jones tied it for UNLV with 1:07 to play, but missed a free throw that would have completed a 3-point play.
Dorian Green then missed a 3-point attempt for the Rams with 41 seconds left. With the shot clock running down, Marshall converted his game-winning shot.
Dejean-Jones and Katin Reinhardt both scored 15 points for the Rebels and Marshall had 11. UNLV improved to 20-7 and is 7-5 in Mountain West action.
Colorado State (21-5, 8-3) was paced by Colton Iverson with 16 points.