For the Cubs, meanwhile, the misery continued. They dropped their sixth straight to match their longest skid this season, and they never regrouped once the White Sox started knocking the ball out of the park.
Back-to-back homers by Beckham and Dunn leading off the fourth gave them a 2-0 lead. Flowers made it 3-0 with a drive to start the fifth off Paul Maholm (4-3), giving the White Sox three homers for the second straight game and Peavy (5-1) all the support he needed.
The right-hander struck out seven and walked two over 6 1-3 innings. He helped chase Maholm during a two-run seventh, grounding into a force and scoring on a sacrifice fly, and he left to cheers with a runner on first after retiring Ian Stewart on a fly to right in the bottom half.
It was a charged weekend in Chicago, with Kerry Wood retiring and Konerko getting hit in the face, not to mention the protests in the city surrounding the NATO Summit.
There was heightened security outside Wrigley Field. Inside, it was more of the same.
Peavy shook off a rough outing against Detroit and got back to dominating.
Maholm got hit hard, allowing five runs and nine hits over 6 1-3 innings after going 4-0 in his previous five starts.
He was sailing along until Beckham lined the first pitch of the fourth to the street beyond the left-field bleachers for his fourth homer. Dunn followed with a drive to center on a 2-2 pitch for his second home run in as many games and 43rd against the Cubs. Among active players, only Albert Pujols has more with 53.
After Peavy escaped a bases-loaded jam in the bottom half, Flowers added to the lead when he started the fifth with his second homer. He also came around on Peavy's grounder after leading off the seventh with a double.
Notes: Although the team has not announced his signing, manager Robin Ventura said veteran INF Orlando Hudson is on his way and that 3B Brent Morel is likely headed to the disabled list because of lower back soreness. A four-time Gold Glove second baseman, Hudson was waived Thursday by San Diego. He will probably see time at third. ... Gavin Floyd is scheduled to start Tuesday, with P.J. Walters going for the Twins. ... Matt Garza starts Monday for the Cubs against Houston, with Bud Norris taking the mound for the Astros. ... Manager Dale Sveum said the Cubs will soon discuss calling up Anthony Rizzo from the minors. It's not hard to see why, considering he's batting .353 with 14 homers and 39 RBIs for Triple-A Iowa. "That's definitely going to be talked about," manager Dale Sveum said. "He's done everything he can down there, but when you bring somebody up like that he's got to play every day so that's the million dollar question. How do we get him playing time?" ... RHP Carlos Marmol (strained right hamstring) and C Steve Clevenger (right oblique) start rehab assignments in Iowa on Monday.