Smith was recruited from Grand Blanc High School in Grand Blanc, Michigan by Michigan coach Bo Schembechler. He also played high school football for Swartz Creek prior to transferring to Grand Blanc for his senior year, joining his former high school coach. Smith was considered a running quarterback and while he employed speed, agility and, good field vision, he was also a competent passer. He started all 12 games for the 1981 Wolverines and led the team to a record of 9–2 in the regular season and a win over UCLA in the 1981 Bluebonnet Bowl. He again started all 12 games at quarterback for the 1982 Wolverines, leading the team to a record of 8–3 in the regular season, and a berth in the 1983 Rose Bowl, where the Wolverines lost to UCLA, 24–14. Receiver Anthony Carter was Smith's main target in 1981 and 1982, earning All-American honors both years. As a senior in 1983, Smith threw four touchdown passes in a game against the Purdue Boilermakers. He led the 1983 Wolverines to a 9–2 record in the regular season and a berth in the 1984 Sugar Bowl, where the Wolverines lost to Auburn, 9–7. Smith was 26–10 as a starter for the Wolverines and passed for 42 touchdowns. He rushed 329 times for 1,736 yards. When he finished his career at Michigan, he was also the team's all time leading passer, a record that has since been surpassed.