It was the first-ever win in Boulder for the Beavers (14-17, 4-14 Pac-12). They were 0-6 before Nelson closed out a tight game on a layup with 15 seconds remaining, sending the crowd heading for the exits.
Spencer Dinwiddie had 18 points for the Buffs (20-10, 10-8), who were attempting to tie the school record for wins in the regular season, a mark held by the 1996-97 squad that featured Chauncey Billups.
After the game, coach Tad Boyle said to the fans over the loud speaker, "I apologize for today's performance."
For a second straight game, Colorado played without Andre Roberson, who's sidelined with a viral illness. Boyle hopes to have the nation's leading rebounder back on the court in the conference tournament.