The Twins assigned Oliva to the class-D Wytheville Twins in the Appalachian League, where he played in 64 games and led the league with a .410 batting average, but had a low fielding percentage of .854. After finishing second to Orlando Cepeda in batting average in the Puerto Rico leagues in winter ball, Oliva was sent to single-A Charlotte in the South Atlantic League, where he played 127 games and hit .350 with 17 home runs and 93 RBIs. He was called up to the major leagues with nine games left and debuted for the Twins on September 9, 1962, hitting a searing .444 in 12 plate appearances.