Sox right-hander Erik Johnson (1-2, 2.87 ERA) earned his first major league victory after six scoreless innings. He allowed four hits, walked two and struck out eight.
The victory tied their season high for runs in an inning and ended the Sox six-game losing streak.
Twins starter Liam Hendriks (1-3, 6.87 ERA) gave up five hits and three walks in the first inning. Conor Gillaspie, Paul Konerko, Dayan Viciedo and Gordon Beckahm hit RBI singles, and Alexei Ramirez added a two-run base hit.
Hendriks was pulled after walking Alejandro De Aza with the bases loaded and two outs.
In the second inning, Jordan Danks looked to have hit a home run but was ruled a double after review. His next plate appearance was a clear two-run home run in the sixth inning to push the Sox ahead 11-0.
Ramirez hit the fourth Sox home run of the night in the seventh inning for a 12-0 Sox lead.