Salaam attended the University of Colorado, where he played for the Colorado Buffaloes football team from 1992 to 1994. As a junior in 1994, Salaam had one of the best individual seasons in college football history, rushing for a school-record 2,055 yards and becoming only the fourth college running back to run for more than 2,000 yards in a season. He also amassed 24 touchdowns and helped lead Colorado to an 11–1 record, including a 41–24 win over the Notre Dame Fighting Irish in the 1995 Fiesta Bowl, and a No. 3 finish in the final Associated Press Poll. The Buffaloes' only loss of the season was to the Big Eight Conference rival Nebraska Cornhuskers, which finished undefeated and ranked No. 1 in both the Associated Press and United Press International polls at season's end. Salaam had four consecutive 200-yard rushing games during the season, his best effort coming against the Texas Longhorns, when he set a school record with 362 yards total offense in a 34–31 Colorado win in Austin. He was a unanimous first-team All-American and winner of the Heisman Trophy in December, beating out running back Ki-Jana Carter of Penn State and quarterbacks Steve McNair of Alcorn State and Kerry Collins of Penn State. Salaam also won the Walter Camp Award and Doak Walker Award.