Liriano (6-11) yielded only a two-run homer by Trevor Plouffe during the outing against his former teammates, while walking two and striking out nine.
Matt Thornton pitched a 1-2-3 ninth for the American League-leading White Sox, who came into the contest with a one-game lead over the Detroit Tigers.
Paul Konerko led Chicago at the plate, smacking a two-run homer and adding an RBI groundout for three RBI.
Twins starter Samuel Deduno (6-4) allowed five walks and three hits over four frames, surrendering four runs. The right-hander struck out six.
Celebrity Families of 2014 [PHOTOS]