Derrick Marks added 17 points as the Broncos (15-6, 3-4 Mountain West) led wire-to-wire.
Anthony Bennett scored 25 points and Anthony Marshall added 18 points and matched a career-high with 12 assists for UNLV (17-5, 4-3).
The Rebels trailed 73-64 after a 3-pointer by Marks with 3:34 remaining and scored the next eight points, pulling within one on a 3-pointer by Marshall with 33 seconds left. Marks and Drmic each hit two free throws in the final seven seconds.
UNLV forward Mike Moser was ejected with 4:07 remaining in the first half after receiving a flagrant 2 foul for delivering a forearm to the head of Drmic on a breakaway.
Boise State led 42-35 at halftime and boosted its advantage to 55-43 on Drmic’s 3-pointer with 13:18 remaining.