Wilson attended Brigham Young University, where he played for the BYU Cougars football team from 1976 to 1979, and was one of the first in BYU's celebrated line of quarterbacks. Cougars coach LaVell Edwards operated a passing-oriented offense that allowed his quarterbacks to throw the ball almost every single down. Thus, Wilson was able to pile up huge passing numbers in an era when most teams mainly focused on running the ball.
Marc first got a chance to start in the fifth game of the 1977 season, replacing All-AmericanGifford Nielsen, who had gone down after four contests with an injury. During that 1977 season, his sophomore year, he threw for seven touchdown passes in one game against Colorado State University, his first start. After that, he started most of BYU's games over the next two-and-a-half seasons, racking up a 22-4 record, though he did yield a few starts to budding star Jim McMahon. In 1979, he threw 250 completions for 3,720 yards and 29 touchdown passes, becoming the school's first consensus All-American. Highlights of his 1979 season included leading the team to an undefeated regular season and a berth in the Holiday Bowl, where he shared the MVP trophy with Indiana Universitycornerback Tim Wilbur in BYU's 38-37 loss. He finished fourth in the nation in passing efficiency, third in the Heisman voting, and was named the Senior Bowl MVP. Wilson's success paved the way for McMahon, Steve Young, Robbie Bosco, Ty Detmer, and other BYU quarterbacks, all of whom had similar performances in Edwards' system.
In the 1980 NFL Draft, Wilson was selected by the Oakland Raiders. He was a backup to Jim Plunkett on the Raiders' 1980 championship team, then led the team in passing in 1981 before throwing only two passes as a backup to Plunkett in the strike-shortened 1982 season, the team's first in Los Angeles. He took over for Plunkett as the starter midway through the 1983 season but was injured two games later; Plunkett returned and led the Raiders to victory in Super Bowl XVIII in January 1984. Wilson benefited greatly from the USFL: in order to prevent him from leaving the NFL, despite him being a backup player, the Raiders tripled his salary between the 1984 and 1985 seasons. Despite leading the Raiders to the AFC West title in 1985, Wilson never established himself as an elite NFL quarterback; he threw three interceptions in a home playoff loss to New England that year and never played in the postseason again. He was outplayed and replaced by the aging Plunkett in 1984 and 1986, and in 1987 was the quarterback of record in the Raiders' first losing season since 1981. He never ranked among the top quarterbacks in the NFL, and bowed out after two unproductive seasons with the New England Patriots, the latter being a difficult 1-15 year during which Wilson played with a broken throwing hand and separated non-throwing shoulder the entire season. This was a far cry from his outstanding collegiate career at BYU, when 9- and 10-win seasons were typical. He spent the 1988 preseason with the Green Bay Packers.