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LOS ANGELES -- Zack Greinke felt the Milwaukee Brewers were primed for a turnaround. Now he's hoping for an even bigger surge for his team.

Greinke pitched effectively for six innings, Aramis Ramirez and Carlos Gomez each hit a two-run homer, and the Brewers beat the major league-leading Los Angeles Dodgers 6-2 on Thursday night to complete a four-game sweep.

"It was pretty impressive," Greinke said. "They're playing better than they have in a while. But we've been due for something like this for a while, so hopefully it continues. I feel like our offense is clicking and getting enough runs on the board so that we can get on a good roll if we keep pitching like we did in this series."

The Brewers won the season series 6-1 for their best record against the Dodgers since shifting from the American League to the National League in 1998. They are the first visiting team to sweep a four-game series at Chavez Ravine since August 1993.

"We played four good games. We got great pitching, great starting pitching, and we got some timely hitting," manager Ron Roenicke said. "Having four games against these guys in their ballpark, we had to play four great games to beat them. And we did. This should give us a lot of confidence. We should be headed in the right direction. When we play our game, we can compete with anybody."

The Brewers won the finale without NL MVP Ryan Braun, who was scratched because of tightness in his right Achilles tendon. He first experienced it May 1 at San Diego, when he hurt himself sliding into second base a day after hitting three home runs against the Padres, and has been playing through it ever since.

"He should be back in there tomorrow," Roenicke said. "If he comes in tomorrow and he's stiff, then we'll change that. But he felt pretty good today and was ready to pinch hit. So he should be ready."

The Dodgers also played without their No. 3 hitter, Matt Kemp, and will be without the slugger for at least a month. The All-Star center fielder, who was runner-up to Braun in last year's MVP voting, was placed on the 15-day disabled list after reinjuring his left hamstring Wednesday night while running the bases in his second game back from the disabled list.

"We were 9-5 without Matt the first time, so regardless of whether he was in the lineup or not, they should feel pretty good about themselves," said Tony Gwynn Jr., who will be playing center field the majority of the time that Kemp is sidelined. "They just swept a first-place team that still leads their division by five games right now. So if the show was on the other foot, I think we'd feel the same way."

Greinke (7-2) allowed a run and nine hits in his Dodger Stadium debut, striking out seven and walking one. The nine-year veteran, who surrendered seven runs and 10 hits over 2 1/3 innings in an 8-5 loss Saturday at Arizona, allowed at least one hit in every inning he pitched and stranded eight baserunners. It was the fourth time in his past five starts that he allowed fewer than two runs.

"There were a lot of singles -- same thing as the last game -- but tonight I made good pitches when I needed to," Greinke said. "I threw a lot of changeups, which I hadn't done in a while. My fastball felt good, and the location was good. I didn't use many curveballs and tried not to use the slider as much."

Chad Billingsley (2-4) struck out eight in six innings for Los Angeles but yielded four runs and six hits. The right-hander is 0-4 with a 5.13 ERA over his past nine starts, a stretch that began with a no-decision at Milwaukee after he beat San Diego and Pittsburgh in his first two outings.

This is the longest winless drought of Billingsley's seven-year career. He was 0-5 with a 5.08 ERA in his final seven starts of 2009, and last season he went 0-1 with a 4.78 ERA during another seven-game stretch.

The Brewers grabbed a 2-0 lead in the second inning when Rickie Weeks hit an RBI single and Taylor Green scored on a fielder's choice grounder by Martin Maldonado.

Billingsley got one of the runs back in the bottom half, driving in Jerry Hairston Jr. with a two-out single for his first RBI of the season. But Greinke minimized the damage, throwing a called third strike past A.J. Ellis with the bases loaded, and Ramirez increased Milwaukee's margin to 4-1 in the third with a two-run homer to left on an 0-2 pitch.

Billingsley retired the first two batters in the fifth before plunking Corey Hart, who was 0-for-14 lifetime against him before that plate appearance. A single by Ramirez and a walk to Green loaded the bases, but the 27-year-old from Defiance, Ohio, escaped the jam by retiring Weeks on a popup.

Game notes

Ellis became the ninth player Dodgers manager Don Mattingly has used in the second spot in the batting order this season and the fourth in the past four games. He was 2-for-5. ... The only other road series the Brewers have won this season was their first one, when they took 3 of 4 against the Cubs. ... Milwaukee CF Nyjer Morgan is 0-for-18 with runners in scoring position. Last season he batted .313 (25-for-80) in those situations with 35 RBIs.