After his "cup of coffee" at the end of the 1981 season, Hrbek would make the team out of spring training and come into his own in 1982, playing well for Twins manager Billy Gardner. Finishing his rookie season hitting .301 with 23 home runs and 92 RBI, Hrbek would finish second in the Rookie of the Year voting (to future Hall of Famer Cal Ripken, Jr.) and be selected to his only All-Star game. Although the Twins would finish 60–102, Hrbek and fellow rookies Tim Laudner, Gary Gaetti, Tom Brunansky, Randy Bush, and Frank Viola would make up the nucleus of the 1987 World Series team. Falling off slightly in his sophomore year (.297, 16 HR, 84 RBI), Hrbek would come up big in 1984, finishing the season hitting .311 (his second-highest career batting average) with 27 HR (his 3rd highest total), 107 RBI (his highest career total), 174 hits (his highest total), and 80 runs (his third highest total). During arguably his career year, Hrbek would power the Twins all season and the team would surprise the rest of the American League West by battling for the division crown. Although the team was as close as 0.5 games out of first place at 81–75, the Twins faded fast, lost their last 6 games, and finished in a tie with the California Angels, three games behind the Kansas City Royals. After the season, Hrbek was recognized for his performance and the team's surprise September run, by his finishing second in the American League Most Valuable Player balloting to Detroit Tigers' closer Willie Hernández.
Since Kent Hrbek's father died of amyotrophic lateral sclerosis (ALS, or "Lou Gehrig's disease") in 1982, he has worked to increase awareness of the disease. Hrbek hosts an annual charity golf tournament in Minnesota to raise money for ALS research and makes many public appearances on behalf of the cause. He also participates in an annual fundraising event called the "Black Woods Blizzard Tour," a snowmobile excursion around northern Minnesota that raises money to fight the deadly disease. Hrbek and his wife, Jeanie Hrbek, are honorary co-chairs of the ALS Association's MN/ND/SD Chapter. He was awarded the Lou Gehrig Memorial Award in 1991 for his efforts.