MINNEAPOLIS (AP) — Jake Peavy won for the first time in more than six weeks with eight shutout innings for Chicago, and the White Sox beat the Twins 7-0 Sunday to sweep a three-game series in Minnesota for the first time in more than seven years.

Brent Lillibridge, Paul Konerko, Alexei Ramirez and Alex Rios each hit home runs for the White Sox, who had lost 29 of 36 games to their nemeses until winning three straight at Target Field this weekend. The backsliding Twins have lost seven of their last eight games overall.

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Peavy (5-5) last picked up a victory by pitching four shutout innings in his first career relief appearance, June 25 against the Washington Nationals, three days after he beat the crosstown rival Cubs with a so-so start. The 2007 National League Cy Young Award winner hasn’t been the same since coming to Chicago in a trade with the Padres, but the 30-year-old right-hander was in such a rhythm it looked like his old San Diego form.

The power surge from his teammates sure helped. The White Sox were averaging barely more than four runs per game when he’s pitched, but little Lillibridge went deep for the second straight day in the second inning and Konerko followed suit in the fourth — both shots to the same section in the second deck above left field off Brian Duensing (8-10).

The White Sox hit only 18 home runs in July, their fewest in that month since 1992. They entered the game still in striking distance of first place, 6 1/2 games behind Detroit in the American League Central.

Peavy, whose start was pushed back by one day, will probably have to play a big part if the third-place White Sox are able to catch the Tigers. He gave up only three hits, all in the first three innings, and Joe Mauer’s double was the only way the Twins got a runner to second base. Peavy struck out six without a walk, hitting one batter.

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Duensing lasted 6 1-3 innings, but he gave up nine hits — Rios had an RBI double to cap a stretch of three straight extra-base hits that started the fourth — and five runs while walking one and striking out four.

One of those runs was unearned, due to a throwing error by Duensing himself in that rough fourth inning. He stopped a soft comebacker hit by Gordon Beckham but sent his throw well wide of first base, blowing an easy out and prompting manager Ron Gardenhire to rub his balding head before letting out a big sigh in the dugout.

That’s the kind of mistake the Twins have been making lately, and being swept by the White Sox is a sure sign they’re struggling. They were 7-1 against their primary division rival this year until this weekend.

Notes: The White Sox are the only AL team with a winning record on the road and a losing mark at home. They’re 14-5 in their last 19 road games, including five wins in a row. … White Sox manager Ozzie Guillen gave struggling DH/1B Adam Dunn a day off against a lefty. Guillen said he hopes Dunn can start fresh and finish strong this season — and that he hopes the slugger will be more aggressive about entering next year in better shape. … The son and daughter of late Hall of Fame outfielder Kirby Puckett took the mound for the ceremonial first pitch, the last in a series of weekend events honoring the 20th anniversary of Minnesota’s 1991 championship team.

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