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LOS ANGELES -- A sudden lack of control by Los Angeles Dodgers closer Jonathan Broxton gave Geovany Soto and the Chicago Cubs a perfect opportunity to make Ryan Dempster's 34th birthday a pleasant one for all concerned.

Soto hit a tiebreaking two-run double in the ninth inning, and the Cubs beat the Dodgers 4-1 on Tuesday night after Los Angeles' Andre Ethier extended his hitting streak to 29 games.

"That was a big win for us," Dempster said. "The guys played great and we got a big hit by Geo in the ninth. If we can come in here tomorrow, then we can have a winning road trip on the west coast -- which is not an easy thing to do."

After getting the first out, Broxton (1-2) walked Marlon Byrd and Carlos Pena on four pitches each. Manager Don Mattingly replaced his struggling closer with Blake Hawksworth, who got an out then gave up Soto's two-out hit to right-center on a 1-2 pitch. Former Dodger Blake DeWitt followed with a pinch-hit RBI single.

Since becoming the Dodgers' regular closer in July 2008, Broxton has saved 60 games in which he got the ball to start the ninth inning. He has allowed at least one baserunner in 34 of those appearances, and had only one perfect inning in which he had three strikeouts. That was May 21, 2010, when he fanned Detroit's Brennan Boesch, Brandon Inge and Alex Avila on 14 pitches to preserve a 4-1 interleague win for Chad Billingsley.

"Broxton's one of our guys, and we just have to figure things out," said Mattingly, who has been in his corner the whole way. "Today it didn't look like the ball was coming out of his hand good and he wasn't throwing strikes. At that point, I can't really leave him out there when he's not throwing the ball over the plate."

Kerry Wood (1-1) pitched a perfect eighth for his first victory with the Cubs since Sept. 18, 2008, and Carlos Marmol got three outs for his eighth save in 10 attempts.

Pitching on his birthday for the first time in his 14-year big league career, Dempster allowed a run and four hits over seven innings with five strikeouts and two walks. The right-hander gave up seven earned runs, four hits and four walks last Thursday at Arizona in the shortest of his 267 career starts, lasting just one-third of an inning.

"I put those first six starts behind me and forgot about them," said Dempster, who came in 1-3 with a 9.58 ERA. "The nice part is that my mom was saying to me: 'April showers bring May flowers.' So hopefully, that's the case. But I'm not going to relax at all after one good outing. Trust me. I'm going to keep pushing and working hard and get on a roll as best I can."

Billingsley allowed a run and four hits over six innings with eight strikeouts and two walks. The only run he allowed was a seventh-inning homer by Pena, his first in a Cubs uniform.

Dempster and Billingsley matched zeros until the sixth. Jamey Carroll led off with a single, advanced on a sacrifice bunt by rookie Jerry Sands and scored on Matt Kemp's line-drive single to center on an 0-1 pitch with two outs.

But Pena tied it with a one-out homer into the Cubs' bullpen in right field on the first pitch. It ended a 3-for-37 rut for the 12-year veteran, who is batting only .164 with seven RBIs in 26 games after signing a one-year, $10 million contract in December as a free agent.

"It appears to me -- and I'm not here all the time -- but if you go down the line, that's your best chance to hit a home run here [at night]," Cubs manager Mike Quade said. "I mean, he's a strong son of a gun and he can leave the park anywhere, but it does seem easier if you go down the line. To me, it was a no-doubter when it left the bat. We needed that and he needed that. So it was great."

Dempster walked his first two batters of the game on four pitches each before getting ahead 0-2 on Ethier, who worked the count full and grounded into a double play on a slider. Kemp followed with a soft liner to first base.

"It was frustrating right off the bat, walking two guys on eight pitches," Dempster said. "Then Geo came out and just kind of calmed me down. Then I went back to being aggressive. I mean, if I'm going to lose, I'd rather lose being aggressive and pitching my way than the way I was going. It was nice to get the double-play ball from Ethier. He's kind of hot right now."

In the fourth, Ethier kept the hitting streak going when he lined Dempster's 1-2 splitter just beyond the leaping attempt of rookie second baseman Darwin Barney and into right field with one out for the Dodgers' first hit.

One pitch earlier, Ethier took a big cut and his bat went flying into the first row of seats behind the first base dugout, bouncing three rows back. Instead of asking the fan who grabbed the bat to return it, Ethier got a new C-271 black ash Louisville Slugger.

"He's one of the premiere players in the game, and he's only getting better," Dodgers second baseman Aaron Miles said. "His confidence level is as high as it can be. He knows all the pitchers in the league well now, so he's got knowledge of them. So he's got that library of knowledge to fall back on, and how guys are going to try to attack him."

Ethier's streak is the longest by a Dodger since Willie Davis' franchise-record 31-game stretch in 1969. A hit in his next game would make Ethier the 44th major leaguer in the modern era (since 1900) with a streak of at least 30.

The All-Star right fielder has gone hitless in only one of the team's first 31 games. That was on April 1 at Dodger Stadium, when he struck out and flied out twice against San Francisco's Jonathan Sanchez and grounded out against Dan Runzler.

Game notes

The Dodgers placed reserve LF Marcus Thames on the 15-day DL because of a strain in his right quad. OF Jay Gibbons, who missed the first 39 games of the season because of vision problems, was reinstated from the DL. ... Barney was named NL rookie of the month after hitting .326 with 14 RBIs in April.