UNLV went on a 9-0 run, capped by McCaw's steal and fast-break dunk, to take a 59-53 lead.
James Webb III had a put-back dunk to pull Boise State to 66-65 with 4:55 left, but UNLV went on a 7-0 run, highlighted by Ike Nwamu's 3-point play after a baseline drive.
Boise State's zone forced a turnover and Nick Duncan hit a 3-pointer at the top of the key to pull to 77-72. McCaw answered with a 3-pointer from the wing and UNLV cruised.
Stephen Zimmerman Jr. added 18 points and Derrick Jones Jr. had 17 for UNLV (13-8, 4-4 Mountain West).
Thompson led Boise State (15-6, 6-2) with 19 points. Webb had 14 points and 11 rebounds and Duncan added 11 points.