SAN FRANCISCO -- The Brewers put the ball in play against Johnny Cueto and good things happened.

Lots and lots of good things.

There was soft contact, hard contact and contact of every other imaginable variety on the way to a 6-2 win over Cueto and the Giants on Tuesday at Oracle Park, as the Brewers opened a double-digit division lead for the first time in a decade and for only the second season in franchise history.

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Brandon Woodruff delivered six quality innings and Lorenzo Cain homered while driving in a pair of runs to extend the National League Central-leading Brewers’ advantage over the second-place Reds to 10 games after Cincinnati was rained out on Tuesday. The only time the Brewers enjoyed a plusher cushion in their division was in 2011, when they led by as many as 10 1/2 games on their way to setting a club record with 96 regular-season victories.

After a 19-9 August that was capped by back-to-back victories behind Corbin Burnes and Woodruff over a Giants team that began the series with MLB’s best record, the Brewers are back to a season-high 29 games over .500 with 29 games to go.

"We can't get complacent,” Woodruff said. “I think we have to keep plugging along. We have to keep playing great baseball. If we think we've got it now, that's not a good mindset."

He added, "Don't get me wrong, it's nice to have a 10-game lead going into the last month of the season."

The Brewers had 10 hits and a 6-0 lead against Cueto before the veteran Giants starter couldn't get out of the fourth inning. Cueto’s only strikeout victim was Woodruff in the third, and that was after Woodruff laced a hit an inning earlier.

The Brewers scored in each of the four innings in which Cueto pitched, starting with a two-run first that included soft singles from Willy Adames (70.9 mph off the bat, according to Statcast) and Christian Yelich (57.8 mph) and a run-scoring groundout from Avisaíl García that dribbled toward third base at 40.9 mph.

Hard contact worked just as well. Cain hit a second-inning home run that left the bat at 103.7 mph and Rowdy Tellez hit a two-out RBI triple at 105.4 mph in the third. Yelich accounted for the loudest contact of all against Cueto when he smacked a 106.9 mph single with two outs in the fourth, then scored all the way from first base on an Omar Narváez bloop single that came off the bat at 84.6 mph, traveled 188 feet and fell in front of a sliding Alex Dickerson in left field as the Giants began to kick the ball around.

“He never got rhythm going,” Brewers manager Craig Counsell said of Cueto, whose start was delayed a day due to non-COVID-19-related illness. “I felt like we made a whole lot of his pitches uncomfortable. And that’s hard to do. We did a nice job against him.”

The Brewers have been doing a better job in that department for a while. In the first three months of the regular season, they had the sixth-worst strikeout rate in baseball -- one per 3.84 plate appearances. They were 16th of 30 teams with 4.32 runs per game.

But over the next two months, Milwaukee hitters had MLB’s eighth-best strikeout rate -- one per 4.68 plate appearances. Runs have followed. The Brewers were fourth in the Majors at 5.1 runs per game over July and August.

Woodruff, meanwhile, denied San Francisco much contact at all while allowing one run on five hits and three walks in six innings and lowering his ERA to 2.35. The Giants had two hits through the first five innings before Brandon Belt put them on the board with a solo home run in the sixth -- his fifth homer against the Brewers in five games in August.

Woodruff stranded a pair of runners to keep the score at 6-1 through that inning before relievers Jake Cousins and Brent Suter finished the game. Cousins struck out Belt and Buster Posey after issuing a pair of one-out walks in the seventh, and Suter covered the final two innings to preserve a second straight victory for Woodruff, who’s affectionately known as “Big Woo” in the clubhouse.

“'Big Woo' was doing 'Big Woo' things. Dominant as usual,” Cain said.

“It shouldn’t go unnoticed,” Counsell said. “He held the best team in baseball to one run in six innings. And through five, he was really dominating, honestly.”

How does a 10-game division lead sound to the manager?

“I don’t see anything different today than yesterday than a week ago, two weeks ago,” Counsell said. “The challenge ahead of us is the next challenge. We have to answer it. There’s a lot of baseball left to be played. A whole month of baseball. That’s a long way to go, and that’s how we have to think about it. When there’s a big body of work left to do, it’s easy to focus on the next day.”

So, on to the next challenge.

September.

“There’s no letup in this team,” Cain said. “We know what we need to do. We have to handle our business. We definitely can’t take September lightly.”