After a college career in which he led the UNC Charlotte 49ers to an NCAA Final Four appearance in 1977, he was drafted by the Boston Celtics, who were coming off a championship season. After coming off the bench his rookie year, he was elevated to a starting small forward position for the 1978-1979 season, a disappointing 29-53 team on which Maxwell was the lone bright spot. The following year, Larry Bird joined the Celtics, and the team started a resurgence that saw them become the dominant team of the 1980s. Maxwell and Bird were joined in the 1980-1981 season by starting center Robert Parish and rookie forward Kevin McHale, a year in which the team won the NBA championship and which Maxwell was named Finals MVP. Maxwell and McHale would compete for the starting forward position over the next several seasons, with McHale winning the starting job and Maxwell being traded to the Los Angeles Clippers just prior to the 1985-1986 season. Maxwell would play for a season and a half for the Clippers, before being traded midway through the 1986-1987 season to the Houston Rockets, where he would finish out his career before retiring after the 1987-1988 season with over 10,000 points scored over his career. Since retiring as a player, he briefly coached the Long Island Surf of the United States Basketball League before starting his career as a radio broadcaster, serving as the color commentator for Celtics radio broadcasts since 2001. His jersey number 31 was retired by the Celtics in 2003.