South Dakota led briefly, 29-28 on a layup by Brandon Bos, but UNLV closed the first half on a 14-2 run to take a 42-31 at intermission.
The Rebels (6-2) connected on 28 of 59 shots from the floor (47.5 percent), hitting 5 of 21 from the perimeter, and collecting 10 steals.
Jelan Kendrick had 13 points for UNLV while Patrick McCaw added 12 points off the bench.
Bos led South Dakota (3-8) with 19 points. Tyler Larson added 14 points, Eric Robertson contributed 12 points off the bench and Casey Kasperbauer kicked in 10 points. Robertson pulled down nine rebounds as the Coyotes outrebounded UNLV 38-33, but turned the ball over 17 times.