The Buffaloes not only won an NCAA game for the first time in 15 years, they upheld the honor of a conference they joined less than 12 months ago.
Colorado is the only team remaining in the tourney from the Pac-12 Conference, which had only two schools in the original field and which became the first power league in the history of the event not to have its regular-season champion participate.
Colorado will meet Baylor in the third round Saturday.
UNLV, seeded sixth in the South Region, fell behind by 19 early in the second half but came back to make a game of it and trailed by just four in the final minute.
Anthony Marshall made an acrobatic layup for UNLV with 21 seconds left and Chace Stanback hit a 3-pointer for the Rebels with 9 seconds left to keep their hopes alive.
Dinwiddie's string of free throws, however, protected Colorado's lead and his last one, coming with 6 seconds to play, clinched the victory.
Colorado, which left the Big 12 to join the Pac-12 this year, got into the tournament thanks to its win over California in the conference tourney Saturday. California received an at-large bid but was knocked out in the first round by South Florida.
Regular-season Pac-12 champion Washington was left out of the event.
Askia Booker led Colorado (24-11) with 16 points off the bench and Austin Dufault had 14. The Buffaloes held on despite turning the ball over 23 times.
UNLV (26-9) got 15 points from Marshall.