The Twins completed a sweep of a day-night doubleheader, having won the opener 7-5.
All five runs in the second contest came on solo homers. Minnesota reached 51 wins for the season with the pair of victories, leaving only the White Sox and Houston having yet to reach the 50-win plateau in the American League.
Chris Herrmann put Minnesota in front in the fourth inning, but Alexei Ramirez and Blake Tekotte hit their home runs in the fourth and sixth frames to give the White Sox the lead.
The homer for Tekotte was his first in what has been a 47-game major league career spread over three seasons.
Josh Willingham tied it in the eighth with his 11th homer of the season and Arcia came through in the 10th on the second pitch of the inning thrown by Dylan Axelrod (4-9).