Geovany Soto had two RBI singles and Melky Cabrera drove in the go-ahead run on a two-out single seventh to give Samardzija (5-4) the victory, sending Twins starter Mike Pelfrey (5-4) to his first loss in seven starts at home this year.
Jose Abreu had a career-high four hits for the White Sox, who stopped another dubious slide by topping three runs for the first time in 10 games. That was their longest such run since 1976.