Parrish's most productive offensive season was 1982 when he posted a .284 batting average with 32 home runs and 87 runs batted in, winning another Silver Slugger Award in the process. He followed that in 1983 with 27 home runs and 114 runs batted in, earning his third Silver Slugger Award and winning his first Gold Glove Award. Parrish was an integral member of the world championship-winning 1984 Detroit Tigers team. Batting as the clean-up hitter, he produced 33 home runs and 98 runs batted in, adding another Silver Slugger Award as well as a second Gold Glove Award to his credentials. He also caught Jack Morris' no-hitter on April 7 of that season. The Tigers led the American League Eastern Division season from start to finish and defeated the Kansas City Royals in the 1984 American League Championship Series before winning the 1984 World Series against the San Diego Padres.