MINNEAPOLIS (AP) — Jake Peavy struck out eight over eight smooth innings, Alejandro De Aza gave Chicago the lead in the eighth with an infield single off Scott Diamond’s leg, and the White Sox beat the Minnesota Twins 3-2 on Wednesday.

Peavy (9-7) allowed five hits and walked two. One of the runs he gave up was unearned, due to a way-wide token pickoff throw to second base in the first inning that sailed into center field. The miscue let Ben Revere move to third, and he scored on Joe Mauer’s groundout.

Danny Valencia homered in the second, but Peavy toughened up after that and had trouble in only two more innings. Denard Span lined into a double play with a runner on third to end the fifth. Mauer popped out to finish the eighth with speedsters Span on third and Revere on first.

Addison Reed pitched a shaky-but-scoreless ninth for his 18th save in 21 attempts, and the White Sox improved to 9-1 in their last 10 one-run games. Brian Dozier flied out to end the game with runners on second and third.

Diamond (9-5) was coming off a three-hit shutout, his first career complete game, in his last start. He had one out in the eighth inning with Tyler Flowers on third, having moved to second on a wild pitch, when De Aza hit a sharp liner that glanced off Diamond’s lower leg. The right-hander was a bit stunned, and his short throw home was well off target as Flowers scored the go-ahead run.

The AL Central-leading White Sox began the first day of the month 2½ games ahead of the Detroit Tigers, against whom they have seven contests remaining this season. This is the fifth time since 2000 the White Sox have started August in first place, and including their 2005 World Series title they made the playoffs in three of the previous four.

They’re in good shape to go again, with the addition of Francisco Liriano to a rotation deepened this year by youngsters Chris Sale and Jose Quintana. Plus, the way Peavy has pitched for most of the season after finally clearing those health hurdles of the last few years has been a significant strength for the White Sox.

Bothered by an elbow injury in 2008, an ankle problem in 2009 and shoulder trouble in 2010 and 2011, Peavy is back on track. This was his 21st start of 2012, his most since 27 turns in 2008 for San Diego. The 2007 National League Cy Young Award winner made a total of only 51 starts in the majors over the three seasons prior to this one.

Peavy hasn’t had much support from the White Sox offense this year, but they did just enough against Diamond to bring him his third victory since May.

De Aza created his own run after leading off the game with a single, moving up on a stolen base, a groundout and Adam Dunn’s sacrifice fly. Flowers almost hit into an inning-ending double play in the fifth after a diving stop by Dozier, but the shortstop had trouble getting the ball out of his glove and Flowers beat the relay throw to first as Rios scored the tying run.

NOTES: The White Sox are off Thursday before beginning a nine-game homestand by hosting the Los Angeles Angels on Friday. RHP Phil Humber (5-5, 5.90 ERA) pitches for the White Sox against Zack Greinke, who will make his second start for the Angels. … Humber has kept his seemingly tenuous starting role for now, with the White Sox using a six-man rotation to protect their young pitchers from overuse. Liriano will make his second start for the White Sox on Sunday, followed by Peavy on Monday. Sale will pitch Tuesday with 10 days of rest, and Quintana will throw Wednesday after an eight-day break. … The Twins start a four-game series in Boston on Thursday. RHP Samuel Deduno (2-0, 3.13 ERA), coming off his strongest of four starts this season, takes the mound to face LHP Jon Lester (5-8, 5.49 ERA). … The Twins are concerned about the pitching elbow of prospect Alex Wimmers, their first-round draft pick in 2010. He is scheduled to travel to Minnesota soon for an exam with team doctors. Tommy John surgery could be next. “He wouldn’t be coming up here if it was any good,” general manager Terry Ryan said. “It’s something we think is serious enough for our people to see him.” Wimmers has pitched in only 19 games over three minor league seasons.

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