The Twins held an early lead over the White Sox after scoring four runs in the second inning Saturday, but Chicago came back with the 5-4 win after taking the lead in the eighth inning.
The Twins had four runs in five hits in the second with Sox pitcher Jeff Samardzija on the mound.
Twins' Chris Herrmann tripled, and Shane Robinson, Santana and Brian Dozier added run-scoring hits, MLB.com reports.
The White Sox added two in the bottom of the second Mike Pelfrey as the starting pitcher. The White Sox brought the score to 4-3 in the third and tied it 4-4 in in the fourth.
White Sox Adam LaRoche and Geovany Soto had their first homers for the team. LaRoche scored in the second, and Soto in the fourth.
The White Sox secured the win with a final run in the eighth.
The Twins are tied with the White Sox in a three-game series, after winning Friday 6-0. They round out the series Sunday afternoon before coming back to Minnesota for Monday's season home opener against the Royals.