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Heading into this week's series, the struggling Milwaukee Brewers didn't appear to be much of a match for the major league-leading Los Angeles Dodgers.

Given how they've roughed up Clayton Kershaw at Chavez Ravine over the past few years, there's a good chance they'll continue proving any doubters wrong.

Milwaukee seeks its first three-game winning streak since early April when it plays the third of four games in Los Angeles on Wednesday night.

The Brewers (21-28) entered this series having lost 10 of 14, but a pair of one-run victories over the Dodgers (32-17) have them on the brink of matching their season-best three-game run from April 9-11.

Ryan Braun's two-run homer in the first inning was all Milwaukee needed in Tuesday's 2-1 victory to spoil the return of Los Angeles slugger Matt Kemp, who went 1 for 4 after missing the previous 14 games with a hamstring injury.

Braun, who beat out Kemp for the 2011 NL MVP award, has been jeered loudly by the Los Angeles fans throughout the first two games.

"I wouldn't say it was something I wasn't anticipating," Braun said. "As a competitor, I kind of makes it fun. It's not something I would choose for it to be, but it certainly makes it enjoyable."

The Brewers will now look to keep rolling against Kershaw (4-2, 1.97 ERA), who has never beaten Milwaukee at home.

The left-hander is 0-2 with an 8.74 ERA in three career starts versus the Brewers at Dodger Stadium. The last time he faced them at home was disastrous, as he allowed seven runs in a career-low 1 1/3 innings May 4, 2010.

Kershaw, though, is one of only two qualifying major league pitchers -- Atlanta's Brandon Beachy (1.77) being the other -- with a sub-2.00 ERA in 2012. The reigning NL Cy Young Award winner got charged with a 3-1 loss to Houston on Friday despite turning in a quality outing, allowing three runs -- two earned -- in seven innings.

"It was typical Clayton, he battled and fought," manager Don Mattingly told the Dodgers' official website. "He hung in the game and gave us a chance to win."

Kershaw will aim for a more similar effort against the Brewers to what he turned in the last time he faced them in Milwaukee, a 5-1 victory Aug. 18 in which he threw eight scoreless innings.

The Dodgers are suddenly stumbling, having dropped four of six. Los Angeles has totaled three runs so far in this series, including a 3-2 loss in Monday's opener. The offense wasn't even sparked by Tuesday's return of Kemp, who is 1 for 17 in his last five games.

"I felt good," Kemp said. "I'm not rusty. I had some pretty good at-bats, so I felt happy with what I did (Tuesday)."

Kemp is 5 for 15 with two doubles lifetime against Yovani Gallardo (3-4, 4.19), who will take the mound for Milwaukee on Wednesday.

Gallardo improved to 2-1 with a 2.13 ERA over his last four starts after allowing one run in 7 1/3 innings of a 7-1 win over Arizona on Friday, but he's never beaten the Dodgers.

The right-hander lost his first three career starts versus Los Angeles while compiling a 10.80 ERA, though he's been much better in his last two outings. Gallardo gave up one run in eight innings of Milwaukee's 2-1 victory over the Dodgers on Aug. 16, then allowed two runs in seven innings of the Brewers' 5-4 win on April 17, but failed to earn a decision in either start.