Roberson, the leading rebounder in the country going into the night, had eight boards and finished 9 of 13 from the floor while helping the Buffaloes (19-8, 9-6 Pac-12) complete a season sweep of the Cardinal after five straight losses in the series between the two schools.
Andy Brown matched his career high with 17 points while Dwight Powell added 12 for Stanford (16-13, 7-9).
Powell nearly pushed the game into overtime after driving around Roberson and dunking the ball on the game's final play, but officials reviewed television replays and ruled that time expired before Powell's bucket.
That ended a wild finish after Colorado trailed most of the game.
Spencer Dinwiddie, who had 19 points for the Buffaloes, scored on a layup with 26 seconds left to put Colorado up 63-59. But when Roberson went to flip the ball to a Stanford player, Dinwiddie reached in to tip the ball away and was called for a technical foul.
Aaron Bright made one of two free throws to pull the Cardinal within 63-60 before Roberson made a pair of insurance free throws.
Colorado has won eight of 10 since opening conference play 1-4 but remains in a logjam in the middle of the conference standings, while Stanford dropped closer to the bottom with its first three-game losing streak at home since 2010.
Chasson Randle got Stanford going early with a 3-pointer and short jumper but it was Powell who provided the signature moment of the night with an emphatic one-handed dunk over a pair of Colorado defenders in the first half. Powell, who started his drive near the left corner of the baseline, was fouled by Jeremy Adams and completed the three-point play to put the Cardinal up 15-4.
Colorado kept it close despite playing its second straight game without 6-foot-10 forward Josh Scott.
Dinwiddie had six points as part of an 11-2 run and Roberson later scored on a layup that tied the game at 27. After a layup by Randle and 3-pointer from John Gage pushed Stanford's lead to five, Dinwiddie and Adams both scored on drives through the key to pull the Buffaloes within 32-31 at the break.
The Cardinal opened the second half with an 11-2 run highlighted by Powell's one-handed 5-footer off an inbounds pass but didn't get much else from their leading scorer. Powell, who went into the night averaging 15.4 points, finished 4 of 11 from the floor.
Colorado responded with its big run to take its first lead since 2-0. Dinwiddie had five points and Roberson, paired against Powell much of the game, made back-to-back 3s to help the Buffaloes go up 51-45.
Roberson's two free throws with 15.1 seconds left gave Colorado a five-point lead but Andy Brown's 3-pointer cut it to 65-63. After Dinwiddie missed the front end of a one-and-one, Stanford called timeout to set up the final shot.
Scott, who is second on the team in rebounding and third in scoring, took an elbow to the head in the Buffaloes' loss to Arizona State on Feb. 16.