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CHICAGO -- Considering how long it had been, it's no surprise that Travis Wood was just a little relieved.

Wood pitched six strong innings for his first win as a starter in more than a year, and the Chicago Cubs beat the White Sox 2-1 on Tuesday night even though Jake Peavy again went the distance.

"Get the first one, get the monkey off your back, and hopefully, you start rolling from here," Wood said.

David DeJesus drove in both runs with a single in the third inning. He led off the ninth with a triple, but Peavy struck out Steve Clevenger looking at a 2-2 pitch with runners on second and third.

The Cubs handed the White Sox their sixth loss in seven games. The North Siders will try to complete the sweep Wednesday after dropping all three at Wrigley Field last month.

The White Sox, meanwhile, were shaking their heads, knowing they are now second in the AL Central and a half-game behind Cleveland after clinching their fifth straight series loss.

"Teams that we feel we should beat that aren't playing that well, we got to show up and take advantage of these opportunities," Peavy said. "Detroit is coming. And we know Cleveland isn't going anywhere."

Wood (1-3) was simply terrific.

He has spent time in the minors this season after coming from Cincinnati in the trade for Sean Marshall, and he finally came away with his first win since a relief appearance for the Reds at Pittsburgh on Aug. 19. He hadn't won as a starter since he beat the Los Angeles Dodgers last June 15, but he finally got one after allowing one run and four hits while striking out five and walking four.

"You always understand the pressures of coming to a new team, especially when you were traded for one of the best relievers in baseball," Cubs manager Dale Sveum said. "You want to impress. It sure seems like he's relaxed out there, making his pitches and making pitches when he has to."

The White Sox threatened in the eighth when James Russell walked Gordon Beckham and Adam Dunn with one out.

Manny Corpas came in, and a sprinting Reed Johnson, who had just replaced Bryan LaHair in right, grabbed Paul Konerko's shallow fly before Alex Rios grounded out to end the inning.

Carlos Marmol worked the ninth for his fourth save in six chances, retiring Orlando Hudson on a grounder to end the game after he walked A.J. Pierzynski.

Peavy (6-3) took another tough-luck loss in his third complete game.

The veteran threw 125 pitches and allowed five hits while striking out five and walking one. He retired 16 straight hitters before Tony Campana singled in the eighth, but came up short again after a 1-0 loss at St. Louis last week.

The Cubs didn't get much going after setting season highs for runs, hits (15) and homers (five) in a 12-3 win on Monday, but they still squeezed this one out.

The White Sox grabbed a 1-0 lead in the second when right fielder LaHair took a poor route on Alexei Ramirez's ground-rule double to the corner after walks to Rios and Dayan Viciedo. Wood then walked Tyler Flowers to load the bases but retired Hudson on a pop fly and struck out Alejandro De Aza to end the inning.

DeJesus came through with the two-run single after Geovany Soto reached on a wide throw by Hudson at third, Campana singled off the pitcher's foot and Peavy uncorked a wild pitch to put them on second and third.

That was enough on a night when Wood dominated. The Cubs also made several neat defensive plays, including one by shortstop Starlin Castro. He raced back for an over-the-shoulder catch on De Aza's bloop to center, bare-handing the ball after it popped out of his glove.

"Unbelievable," Castro said. "I don't know how."

Hudson, meanwhile, was fuming at himself for that bad throw on Soto's grounder.

"I lost the game for the man (Peavy), that's it," he said. "The man threw a hell of a game, I lost it for him. Point blank. Case closed. We lost. My bad. That's it."

Game notes

White Sox pitcher John Danks could begin a rehabilitation assignment in three or four weeks after tests confirmed he has a mild muscle strain in his left shoulder. Two MRIs on Monday showed that Danks has a mild Grade 1 strain of the subscapularis muscle in his left shoulder. There is no tendon or ligament damage and his labrum is intact. ... With Zach Stewart being optioned to Triple-A, the White Sox recalled RHP Dylan Axelrod from the minor league club. Axelrod was with the White Sox from April 27 to May 5, going 0-1 with a 3.52 ERA in three appearances, including one start. He is expected to pitch mostly in long relief. ... Cubs 3B Ian Stewart (15-day DL) received a second cortisone injection to treat a sore left wrist on Monday, this time on top of his left hand. Sveum said he doesn't think surgery is on the table right now. ... Asked if LaHair would have made the catch on Konerko in the eighth, Sveum said, "I don't think LaHair would have gotten to it."