The 17th-ranked Buffaloes won their fourth in a row and are unbeaten in three Pacific-12 Conference outings.
A 3-pointer by D.J. Shelton with eight seconds left brought Washington State within three and Dinwiddie was immediately fouled.
He made 1-of-2 in that trip to the line to give Colorado a 71-67 lead.
Royce Woolridge then hit another long-range shot for the Cougars to cut their deficit to one and Dinwiddie was fouled once more with two seconds left.
Dinwiddie missed both attempts, but the Cougars were not left with enough time to get off a shot.
Washington State forced the overtime on a 3-pointer from Que Johnson with six seconds to go in regulation.
Josh Scott led the Buffaloes with 19 points. Askia Booker had 18 and Xavier Johnson pitched in 14 to boost Colorado to 14-2 for the season.
Washington State (7-8, 0-3 Pac-12) was led by Dexter Kernick-Drew with 14 points.