The Cardinal (8-1) have now won four straight since a 12-point loss at Siena on Nov. 17.
Colorado (5-3) had its three-game winning streak snapped. The team was led in scoring by Marcus Hall with 16. He also had four assists as he logged 40 minutes for the second straight game.
Robin Lopez, the Cardinal's second-leading scorer, didn't score until the 18:48 mark of the second half. He finished with four points and six rebounds. Taj Finger provided a spark off the bench, scoring 11 points, and Hill grabbed a season-high 10 boards.
Colorado was down by three points, 25-22, after Levi Knutson hit a 3-pointer in the closing seconds of the first half.
However, the Cardinal went on a 16-4 run to start the second half to break open the contest.
The Buffaloes were coming off a 60-50 win at Air Force on Thursday night in coach Jeff Bzdelik's emotional return to the academy. Bzdelik bolted from Air Force to Colorado last April. The team had also won back-to-back road games for the first time since the 1998-99 season.
Stanford showed it was comfortable playing at the Buffaloes' slowed-down pace. The Cardinal scored 13 points under their season average.
The Cardinal won a school-record seven games during a busy November. The schedule slows down in December, though, as the Cardinal won't play again until Dec. 19 when they host Santa Clara. The team will squeeze in an exhibition game on Dec. 16 against College of Idaho.
Stanford has been playing without Lopez's 7-foot twin, Brook, who is academically ineligible for the fall quarter. He averaged 12.6 points a game last season and flirted with the idea of turning pro before electing to return for his sophomore season rather than declare himself eligible for the NBA draft.
It was the first meeting between the two schools since the Cardinal's 71-58 win on Nov. 30, 1991. Stanford now leads the all-time series 6-3.