In 1959, his first full season, Allison batted .261 with 30 home runs and 85 runs batted in; led the league in triples (9), was named to the All-Star team, and was honored by being voted Rookie of the Year. When the Senators moved to Minnesota in 1961, Allison became a local favorite, and along with teammate Harmon Killebrew made one of the most dangerous one-two punches in baseball.
In 1963, Allison had 25 doubles, 35 home runs, 91 RBI, led the league in runs scored (99) and in OPS (.911), and earned his second all star berth. He followed this up in 1964 with a 32 home run 86 RBI performance that got him named to his third and final all star team. The next year, Allison suffered a broken left hand when he was hit by a pitch. He missed 91 games, but returned at the end of the season and pinch hit a three-run homer, sending the Yankees to the cellar in the American League.
In 13 seasons, Allison finished in the top ten in home runs eight times (1959, 1961-65, 1967-68). Particularly memorable home run feats included hitting three consecutive home runs on May 17, 1963, combining with Harmon Killebrew to become the first pair to hit grand slams in the same inning on July 18, 1963, and teaming with Killebrew, Tony Oliva, and Jimmie Hall to hit four consecutive home runs on May 2, 1964. He is also well remembered for his backhand diving catch in Game Two of the 1965 World Series. This catch has been called the best catch in Twins history and one of the most spectacular catches seen in the Series.
After retiring, Allison became general manager of Coca Cola's Twin Cities Marketing Division. He later contracted ataxia and died in Rio Verde, Arizona at 60 years of age.