Garret Grayson completed 14 of 21 passes for 173 yards and two touchdowns and Jared Roberts kicked two fourth-quarter field goals after the Rams had fallen behind 17-16 in the fourth quarter.
Grayson outdueled Kansas transfer Jordan Webb, who was 22 of 41 for 176 yards and two TDs for the Buffaloes.
McElwain, the former offensive coordinator at defending national champion Alabama, became the first Rams coach to win his debut since Jerry Wampfler in 1970. None of other 12 Rams coaches who have faced Colorado had ever beaten the Buffs on their first try.
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