White Sox get slugged 12-3 by Cubs
But White Sox manager Robin Ventura said he wasn't too concerned about Stewart's struggles in his first start of the season.
"He's been used a lot (in relief) and that's partly my fault," Ventura said. "And he's been good. It's just one of those days for him and I still trust him.
"It doesn't matter how hard you throw, guys are going to hit you if you miss location."
Bryan LaHair and Alfonso Soriano homered as the Cubs broke a three-game losing streak with the road win.
With winds gusting to 41 mph the Cubs also had season highs of 15 hits and 12 runs.
Starlin Castro and Luis Valbuena homered and had three hits apiece for the Cubs and Geovany Soto added a solo shot in his first game back from the 15-day disabled list.
Matt Garza (3-5) allowed home runs to Paul Konerko and A.J. Pierzynski, but limited the damage to three runs over six innings to earn the win.
Stewart (1-2) was tagged for six runs and nine hits, including four homers, over 5 2-3 innings.
The Cubs exacted some revenge on the White Sox, who earned the sweep when the teams met at Wrigley Field May 18-20. The White Sox had won seven of the last eight matchups against the Cubs.
The Cubs scored 11 runs with four homers on Memorial Day against the San Diego Padres, and had 14 hits four times.
The White Sox have lost five of their last six and nine of 13 overall.
Making his first appearance of the season in right field, LaHair passed an early test with a retreating catch to rob Gordon Beckham of extra bases in the first inning.
The big lefty hit his 13th homer of the season with one on and two outs in the third.
Castro added a two-run shot in the fifth, and Soriano hit a solo homer two batters later.
Soriano's 440-foot blast to straightaway center was his 13th of the year -- all have come since May 15. He added an RBI single in the Cubs' six-run seventh.
His four homers and 10 RBIs are franchise records for a designated hitter.
"We had big hits," Soriano said. "LaHair had a big homer, Castro had a big homer. That's the most important thing, I hope we continue doing that.
"We see the ball good in this ballpark. It's different. I feel comfortable in this ballpark."
Stewart was roughed up in his first start of the season. Pitching in a long-relief role this season, he was called upon to give aces Chris Sale and Jake Peavy extra rest.
Stewart was pulled in the sixth after allowing his fourth homer of the game to Soto, who had arthroscopic surgery to repair a torn meniscus in his left knee.
"I just made a few bad pitches, pitches I wouldn't want to make in that situation and they did their job," the right-hander said. "There were a few opportunities that came about and I couldn't make the pitch and they did what they were supposed to do with it."
Will Ohman gave up two runs in 2-3 of an inning of relief, and Nate Jones gave up four runs without retiring a batter in the seventh.
Valbuena's three-run shot capped the Cubs' big inning.
Pierzynski hit a solo homer in the fifth, his 12th of the season and Konerko hit his 13th, a two-run shot, in the sixth.
Garza gave up three runs and five hits over six innings. He struck out six and issued one walk.
In a crosstown series that typically sells out or comes close, Monday's game drew just 33,215 fans on a hot, breezy night. It was the smallest Cubs-Sox crowd since interleague play began in 1997.
Notes: The Cubs placed RHP Ryan Dempster (right lat tightness) on the 15-day DL and recalled RHP Scott Maine from Triple-A Iowa. . C Welington Castillo was optioned to Iowa to accommodate Soto's roster spot. . White Sox OF Kosuke Fukudome (strained right oblique) The White Sox agreed to terms on a minor-league contract with first-round draft pick Courtney Hawkins. Hawkins, the 13th overall pick, will report to Advanced Rookie League Bristol. . Chicago Bulls Hall of Famer Scottie Pippen threw out the first pitch. . The Cubs will send Travis Wood (0-3, 4.58 ERA) to the hill on Tuesday against Peavy (6-2, 2.91).