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MILWAUKEE -- Zack Greinke came to Milwaukee for the thrill of a playoff race. Instead, the Brewers are way out in front with just over a month to go.

Greinke pitched effectively into the eighth inning to remain perfect at home, Corey Hart homered for the second time in as many days and Milwaukee held on to sweep the Chicago Cubs with a 3-2 win Sunday.

The NL Central-leading Brewers stayed a franchise-best 10½ games ahead of St. Louis after the Cardinals beat Pittsburgh 7-4. Milwaukee and St. Louis play a three-game series at Miller Park beginning Tuesday.

"The double-digit lead is hard to believe, it seemed like just the other day we were one back. That is weird to see," Greinke said. "We're enjoying playing, but nothing's locked up yet."

Greinke (13-5) improved to 10-0 at home as the Brewers kept up their remarkable run. They were in third place on July 25 before winning 27 of 32 overall.

Milwaukee has won 21 times this month, tying the franchise mark for most victories in a month set in June 1978.

"They know where we are," Brewers manager Ron Roenicke said. "But their focus is so much on that game, that day, I don't think we're worried about where that end is going to come."

It became a tense ninth when Tyler Colvin homered off Brewers closer John Axford with one out.

Axford walked Marlon Byrd before getting Alfonso Soriano to hit a warning track flyball for the second out. Third baseman Casey McGehee then misplayed pinch-hitter Reed Johnson's grounder to put two on.

McGehee bobbled the next ball, too, by pinch-hitter Geovany Soto, but recovered to tag out Byrd and give Axford his 40th save this year.

"It seemed like it was spinning for a little while up there," Axford said. "I'm glad it went in his glove, that's for sure."

Greinke gave up four hits, not allowing any until Byrd's fifth-inning bloop. In the bottom of the inning, Greinke singled, stole second for the first swipe of his career and scored on Hart's homer.

In the eighth, Greinke left with two out and a runner on second for Francisco Rodriguez, who allowed an RBI double to Darwin Barney that made it 3-1 before Aramis Ramirez grounded out to end the inning.

Greinke, the 2009 AL Cy Young winner who was traded from Kansas City in the offsesason, extended his franchise-best home start. He has a 2.96 ERA over 12 starts at Miller Park, all wins for the Brewers.

Milwaukee won for a major league-best 50th time at home this season.

"That's a lot of wins. Yeah, the guys continue to play well here," Roenicke said. "Started again with great pitching from Zack."

Just like the day before, the Brewers scored in the first against the Cubs.

Hart extended his hitting streak to 11 games with a single, reached second on a sacrifice bunt and scored on Ryan Braun's double.

Greinke's steal came when Cubs starter Casey Coleman (2-7) never looked over at him. Hart reached safely for the 10th straight plate appearance with his home run to left.

Greinke struck out seven and walked two.

"Fastball command was pretty good, but changeup was as good as it's been and the curve and slider were usable," Greinke said. "They hit a lot toward our guys, and that made it easier."

It was another dismal series in Milwaukee for the Cubs, who won their first game at Miller Park this season and lost the final eight. Ramirez's 16-game hitting streak and Starlin Castro's career-high 11-game streak ended, but Cubs manager Mike Quade didn't see much of it. He was ejected by plate umpire Bill Miller after Ramirez struck out in the first.

"I wanted to make sure (Ramirez) didn't get thrown out," Quade said. "I didn't want to get thrown out myself. Rammy rarely says anything so I just wanted to make sure that Bill wasn't upset with him, to make sure we had him for nine innings."

Game notes

According to STATS LLC, Greinke joined Cliff Lee of the Phillies and Ted Lilly of the Dodgers as the only pitchers with stolen bases this season. ... The Brewers have a day off Monday before facing the Cardinals. Brewers RHP Shaun Marcum (11-4, 3.38 ERA) is expected to face RHP Edwin Jackson (3-2, 3.99) in the opener. ... The Cubs open a three-game series in San Francisco on Monday. Cubs RHP Randy Wells (5-4, 5.53) will take the mound against Tim Lincecum (12-10, 2.46).