CHICAGO (AP) -- The Chicago Cubs are beginning to get excited about their rotation again.
"Our pitching going into the season was our strength, especially our starting pitching. It's nice to have them all back," manager Dusty Baker said.
Jerry Hairston also drove in a run with a single as the Cubs won their third straight.
Zambrano (5-4) was 1-3 in his previous eight starts. Since pitching seven scoreless innings in his last win at San Diego on June 5, he had allowed 18 runs over 13 innings in three starts.
Zambrano, who gave up eight runs in 1 2/3 innings in his previous start at Milwaukee last Wednesday, was much stronger in his rematch against Davis (9-7).
"The only change was the location," Zambrano said. "I was ahead in the count a lot of times today. In Milwaukee, I was all over the place. When I came up to look for the zone, they hit the ball hard."
Baker was impressed with Zambrano's determination to bounce back.
"He knew what he had to do after what happened," Baker said. "He pitched a heck of a ballgame. He mixed his pitches real well and finally got Carlos Lee out."
The Brewers put two runners on only once -- when Geoff Jenkins
led off the eighth with a walk and Miller followed with a single to right.
Jenkins was thrown out at third by Derrek Lee on Trent Durrington's bunt. Cubs center fielder Corey Patterson got Zambrano out of the jam by making a diving catch of Brady Clark's liner and doubling up Miller at second to end the inning.
"If that ball gets by him, both those runners score," Baker said. "But it ended up being a double play. It worked out like you like it. 'Z' got eight innings and [Ryan] Dempster got the save."
"That was exciting," Zambrano added. "He came out of nowhere to make that play."
Dempster worked a perfect ninth for his 12th save in 13 chances.
The shutout was the second straight for the Cubs, who have not allowed a run in 25 innings. They blanked the White Sox on one hit Sunday, when Prior returned from the disabled list and pitched six innings.
Wood will come off the DL on Wednesday to start against the Brewers.
"Hopefully, Woody will come through tomorrow with a big game," Baker said.
Zambrano outpitched Davis, who allowed just two runs and four hits in seven innings. The left-hander struck out nine and walked two.
"I felt like I had all my pitches," Davis said. "I made a good pitch to Derrek Lee. I went away, away, away -- one ball in on him and he hits a home run.
"He just outpitched me, that's all," he said.
Zambrano didn't allow a hit until Overbay grounded a single up the middle leading off the fifth. Through the first four innings he walked two and, thanks to a double play in the second, faced only 13 batters.
Davis got the second hit off Zambrano when he beat out an infield single to start the sixth.
Derrek Lee's high fly to left with two outs in the third reached the bleachers for a solo homer that stretched Chicago's lead to 2-0.
Patterson was in the leadoff spot for the sixth straight game. ... Baker juggled the lower half of his batting order looking for added offense. Among his moves was bumping catcher Michael Barrett up to fifth. The Cubs' Nos. 5-8 hitters entered a combined 8-for-63. ... Derrek Lee hadn't homered since last week, when he hit four in a four-game series at Milwaukee. ... Davis entered 5-1 in his last seven starts. ... Milwaukee shortstop Bill Hall was ejected for throwing his bat after a called strikeout in the seventh.
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