The Ducks took a seven-point lead on Carlos Emory's dunk with 4:31 to play and they did not score again. They missed five shots and turned the ball over four times while collapsing down the stretch.
Oregon won its first seven Pacific-12 Conference games this season, but has now lost three in a row to Stanford, California and the Buffaloes.
Roberson had a layup attempt blocked by Arsalan Kazemi with time running down, but grabbed the rebound and laid it in to put Colorado in front. Oregon's E.J. Singler missed a turnaround jumper with 4 seconds remaining.
Roberson, with 10 points, was the only Colorado player in double figures during the defensive struggle. Oregon scored just 19 second-half points, both sides shot 36 percent from the field and the teams combined to make 7-of-27 shots from 3-point range.
The Buffaloes improved to 15-7 and are 5-5 in Pac-12 play. Singler and Emory both scored 14 points for the Ducks (18-5, 7-3).