Oliva batted .342 in three minors seasons, winning one batting title and missing another by .0001 of a point. He was signed by Minnesota as a non-amateur free agent in 1961 and made his debut in 1962. After hit a combined .438 (7-for-16) in two seasons, in 1964 he led the league in batting average (.323), hits (217), runs (109), total bases (374), doubles (43), extra-base hits (84), and multi-hit games (71). He was selected as the Rookie of the Year and probably should have won the MVP award, but third baseman Brooks Robinson got the honors with a career year both at the plate and on the field.

In 1965 Oliva won his second straight batting title with a .321 BA. Behind him, only two hitters reached the .300 mark: Carl Yastrzemski (.312) and Vic Davalillo (.301). Oliva added 16 home runs, 98 runs batted in, 107 runs, and led the league in hits (185). The next year, he was leading the league with .328 at the end of July, but a 3-for-30 slump in the middle of August cost him a chance at his third straight batting title. He finished with .309 and was second to Frank Robinson (.316).

The rest of the decade Oliva was hampered by knees, legs, and shoulder injuries. He missed 34 games in 1968, rebounding the next two years with .309, 24 homers, 101 RBI, and .325, 23, 107, respectively. He missed all but ten games of the 1972 season, which required season-ending surgery. In 1973, when the American League adopted the designated hitter, he was able to extend his career until 1976.

In 15-seasons career, Oliva batted .304 with 220 homeruns, 947 RBI, 870 runs, 1917 hits, 329 doubles, 48 triples, and 86 stolen bases in 1676 games. After retiring, he served as a batting coach for the Twins.

It is debated by many that Oliva deserves induction into the Baseball Hall of Fame because of his great offensive numbers in years that were heavily dominated throughout the league by great pitching, which make his consecutive batting titles even more impressive.