Brian Dozier added a career-high four hits as the Twins won for the seventh time in nine games.
Avisail Garcia had three hits for Chicago, which has lost five straight and been outscored 39-10 in those games.
Ryan Pressly (1-0) pitched 2 2-3 innings of hitless relief. Starter Mike Pelfrey allowed five hits and two earned runs in 3 1-3 innings, hitting three batters and walking two.
John Danks (1-3) lasted just 2 1-3 innings and gave up seven runs, three earned, and eight hits. He struck out three and committed two errors.