After another brilliantly pitched game fell to the wayside, Ryan Dempster found nobody to blame but himself.

George Kottaras hit a two-run homer in the seventh inning, and Yovani Gallardo outdueled Dempster as the Milwaukee Brewers beat the Chicago Cubs 2-1 Wednesday for their third straight win in the four-game series.

"I could have won that game if I make a couple better pitches in the seventh inning," Dempster said. "Games like those are the ones where a mistake can end up costing you the game.

"I made a mistake and it cost us the game."

Backed by Starlin Castro's first-inning sacrifice fly that followed David DeJesus' double, Dempster (0-1) had a three-hit shutout before Mat Gamel doubled leading off the seventh. Kottaras, Milwaukee's backup catcher, followed with his second homer this season.

Dempster took a no-decision in his first start of the season after allowing one run over 7 2-3 against the Washington Nationals.

"I knew today it was going to be tough to win a game," Dempster said. "I'm kind of upset with myself because we have a chance to win that game if I don't give up that home run."

Dempster didn't have much leeway, as the Cubs offense faltered again. He's received just one run of support in each of his starts.

Cubs hitters struck out 12 times and left eight runners on base. They were hitless in seven at-bats with runners in scoring position.

"We're all trying to have good at-bats, we're all trying to be aggressive," said Geovany Soto, who whiffed with two on and nobody out in the seventh. "We're going as aggressive as we can and trying to do something at the plate. Sometimes it's going to go like that."

Gallardo (1-1) allowed five hits in seven innings, struck out six and walked two, getting 11 groundball outs.

It was a welcomed improvement, as he was battered for six runs in 3 2-3 innings in his season debut against the St. Louis Cardinals.

"I was a little more aggressive with the fastball down in the strike zone, moving it around in and out," the 26-year-old righty said. "The slider was the best slider I've had in a while. I was able to command it and get ground balls whenever I needed them."

Francisco Rodriguez worked around a pair of walks in the eighth, and John Axford pitched a one-hit ninth for his second save, dropping the last-place Cubs to 1-5.

Dempster allowed two runs, five hits and three walks in 6 2-3 innings with five strikeouts.

Milwaukee gave Ryan Braun, Corey Hart and regular catcher Jonathan Lucroy a day off from the starting lineup.

Making his first big league start, Brewers leadoff hitter Norichika Aoki reached on a single and a walk, seeing 29 pitches over four plate appearances. Aoki was a three-time batting champion and six-time Gold Glove winner during seven seasons with the Yakult Swallows in Japan's Central League.

NOTES: Brewers manager Ron Roenicke said Braun and Lucroy both had rib tightness that they could have played through. ... Dempster struck out Kottaras in the fifth inning to become the 12th pitcher to strike out 1,000 for the Cubs. ... Chicago RHP Kerry Wood struck out the side in the eighth after two outings in which he combined to allow three earned run and three walks in one innings. ... Chicago's Matt Garza looks for his first win of the season in Thursday's series finale against Zack Greinke, who threw seven shutout innings vs. St. Louis in his season debut. Garza was 2-1 with a 4.35 ERA against Milwaukee last year.