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CHICAGO -- Not even CC Sabathia could stop the Milwaukee Brewers' late-season slide. A managerial change didn't work either.

The Chicago Cubs moved closer to their second straight division title Tuesday night, becoming the first NL team to beat the Brewers' big left-hander and spoiling Dale Sveum's debut as interim manager with a 5-4 victory.

"It's very special. Everybody knows who CC is," Chicago's Alfonso Soriano said.

Sabathia (9-1), acquired by the Brewers on July 7, had won 12 straight decisions overall, dating to a June 5 loss to Texas when he was still pitching for Cleveland. He gave up four runs and nine hits in seven innings, including Soriano's 29th homer in the seventh.

Sveum replaced Ned Yost, who was fired Monday in a shocking move by a team that is still 15 games over .500 with 11 left. But the Brewers' late-season struggles won't go away. They lost for the 12th time in 15 games and fell one-half game behind New York for the NL wild card.

"We've been in that position for quite a long time and we lost it tonight. We have 11 games left to get it back," Sveum said, calling his first managerial experience in the big leagues "actually kind of cool."

"I had a lot of anxiety all day long, as well as yesterday. Right as the game started it seemed that everything calmed down."

Prince Fielder hit his 31st and 32nd homers for the Brewers, a prodigious two-run shot off Dempster in the sixth that cleared the right field bleachers and a solo shot off Carlos Marmol leading off the eighth. In the ninth with two on, the Milwaukee slugger was struck out by Kerry Wood to end the game.

Henry Blanco's pinch-hit RBI single in the eighth pushed Chicago's lead to 5-3 and it turned out to be a big run.

Milwaukee's Ray Durham hit a two-out RBI double off Wood in the ninth to make it 5-4 before Ryan Braun's infield single put runners at the corners and brought up Fielder.

On a 3-2 pitch with Wrigley Field roaring, Wood got a called third strike past Fielder to get his 31st save in 38 chances.

"He made a good pitch," Fielder said. "He's one of the best closers and it was fun going at each other. It's part of the game. Somebody has to win."

Fielder was called out on a breaking ball, the 10th pitch of his at-bat.

"I kind of got away with one there. It was a pretty good pitch to hit. I think he was geared up for fastballs," Wood said. "With Fielder up there, there is a threat of making a mistake and obviously we've seen what he can do with those."

Ryan Dempster (16-6) pitched six innings for his career-high 16th win as the Cubs reduced their magic number for clinching their second straight NL Central title to four.

"That's huge, to beat a guy who hadn't lost in our league this year. It feels good to accomplish something like that," Dempster said.

"I know how big a game it is," Sabathia said. "I think from here on out every game is a big game. ... The season doesn't end tomorrow. We still have 11 games left to try to get in. ... Tonight I needed to be better than I was."

Following two dominating performances by Cubs' starters, Dempster allowed two runs and seven hits in six innings. He walked one and struck nine.

Carlos Zambrano pitched a no-hitter against Houston on Sunday at Milwaukee's Miller Park, and Ted Lilly had a no-hitter until the seventh on Monday before combining with three relievers on a one-hitter against the Astros.

Dempster allowed a first-inning double to Fielder and then retired 11 straight before Craig Counsell singled in the fifth. Jason Kendall followed with a single and the Brewers loaded the bases when Dempster fumbled Sabathia's sacrifice for an error.

But Mike Cameron, moved into the leadoff spot to shake up the moribund offense, then bounced into a double play to end the inning on a play that brought Sveum out for his first argument. His beef with first base umpire Joe West was apparently that first baseman Derrek Lee pulled his foot off the bag while taking the throw from third baseman Aramis Ramirez.

West ejected Milwaukee first base coach Ed Sedar before the start of the top of the sixth.

Soriano doubled leading off in the first, moved up on a grounder and scored easily when Lee's long drive to center went off Cameron's glove for another double.

Ryan Theriot and Lee had consecutive singles to start the Chicago third before Ramirez lined a two-run double into the left field corner for a 3-0 lead.

Game notes

Dempster is 13-3 at Wrigley Field, the most home wins by a Cub since Fergie Jenkins won 13 in 1971. ... Fielder has 12 multihomer games in his career.