Alex Kirilloff homered, doubled and drove in four runs for Minnesota in the opener of a three-game series.
Ryan Jeffers also hit a home run and Edouard Julien had a single, two walks and two runs for Minnesota, which improved to 6-2 since the All-Star break.
Joe Ryan (9-6) picked up his second win in his past 10 starts, allowing four runs on seven hits and a walk over six innings while striking out 10.
Andrew Benintendi hit a home run and had two hits and Yasmani Grandal also homered for Chicago, which took its third loss in four games. Eloy Jimenez and Elvis Andrus each added a double, a single and a run for the White Sox
Lance Lynn (6-9) gave up nine runs, six earned, on eight hits and three walks over 6 2/3 innings. He struck out six and allowed four home runs to increase his major-league-leading total to 28.
Chicago took the lead when Benintendi clobbered the first pitch of the game 396 feet into the second deck in right for his second homer of the season.
Minnesota answered with five runs in the bottom of the first. Julien singled with one out to extend his hitting streak to nine games and then scored on Kirilloff's eighth home run of the season.
Max Kepler followed with an infield single and went to second on a walk to Matt Wallner. Buxton then snapped an 0-for-26 streak with a 427-foot homer deep into the bullpen in left-center.
The Twins extended their lead to 7-1 in the fourth on solo home runs by Buxton, his 17th, and Jeffers, his fifth
The White Sox made it 7-2 in the fifth when Andrus doubled off the wall in left-center and scored on a single by Tim Anderson
Chicago cut it to 7-4 in the sixth on Grandal's two-run home run, a 394-foot drive into the plaza in right. The Twins extended the lead back to five runs in the seventh on a two-run double by Kirilloff
--Field Level Media