Making his debut in 1974 at the age of 20, Parrish became a solid hitter as a third baseman in the 1970s and 1980s, hitting 20 or more home runs in a season 5 times during his Major League career. He was a two-time All-Star, and in 1979, he was named the Montreal Expos Player of the Year after batting .307 with 30 homers and 82 runs batted in. Parrish is the only Montreal Expos player to ever hit three home runs in one game on three separate occasions (May 29, 1977, July 30, 1978, and April 25, 1980). In the May 1977 game against the Cardinals, he went 5–for–5, batting in 5 runs in a 14–4 victory. In the April 1980 game, he drove in all 7 runs for Montreal in an 8–7 loss to Atlanta.