MILWAUKEE -- The Brewers pushed a season-high 10 games over .500 and five games up on the rest of the National League Central with a 6-4 win over the Cubs on Thursday at American Family Field.

It’s amazing what team speed can do -- especially when it’s mixed with a dose of power.

“That’s the kind of team we have this year,” said Brewers catcher Gary Sánchez after deciding the game with the latter. “We’ve got a fast team. I’m fast myself.”

Statcast might have something to say about Sánchez’s self-assessment, but there’s no doubt that being fleet-footed on the bases set up the Brewers for victory. Third-base coach Jason Lane’s aggressive send of outfielder Sal Frelick in the second inning opened up a three-run scoring rally and Blake Perkins and Brice Turang combined to manufacture one go-ahead run in the seventh. But it was the not so fleet-footed Sánchez who put the Brewers ahead for good with a full-count, two-out, two-run home run in the eighth to cap his three-RBI afternoon.

All of the Brewers’ runs scored with two outs; seven of their nine hits came with two strikes.

“You’ve got to have multiple ways to beat a team,” Milwaukee manager Pat Murphy said. “‘Offense’ means you’re capable of doing a lot of different things. I think it got proved out a little bit again today. [The Cubs] are coming off a losing streak and they’re swinging the bat way better than they did during that streak, and we had to do everything we could to win that ballgame.”

By taking three of four games in the series from Craig Counsell and the Cubs, Milwaukee (33-23) pushed Chicago (28-29) down to third place in the NL Central standings. The idle Cardinals (27-27), winners of 12 of their last 15 games, moved up to second place.

“I think there’s a little something extra to [this series],” said Brewers starter Colin Rea, who pitched parts of at least six innings for the eighth time in 11 outings and came away with a no-decision. “Today was one of those hard-fought wins. We just kept competing.”

The Brewers won despite their best reliever, Bryan Hudson, surrendering game-tying home runs in successive innings in the seventh (Seiya Suzuki’s two-run shot) and the eighth (Christopher Morel’s two-out solo homer). That, after Hudson allowed only one homer in his first 20 appearances this season including none in his last 17 games -- a dominant stretch in which Hudson had a 0.36 ERA.

Hudson’s catcher helped bail him out. The Brewers signed Sánchez to mash against left-handers but he hit Thursday’s go-ahead shot off a Cubs righty, Tyson Miller.

“He’s going to have some strikeouts, but he’s dangerous and everybody in the league knows it,” Murphy said. “He’s kind of shoved it in our face a little bit, like, ‘Hey man, I can hit more than lefties.’ It’s pretty cool.”

Just as cool were the runs the Brewers manufactured.

Against Cubs starter Jameson Taillon in the second inning, Sánchez made it a 1-1 game by lifting a sacrifice fly for the second out of the frame -- but Frelick made it a bigger inning by punching a single that wound up producing two more runs. Frelick scored all the way from first base with a perfect slide on Joey Ortiz’s double, and Ortiz then scored on Perkins’ base hit to give the Brewers a 3-1 lead.

“If Sal is out there, like a lot of guys would be -- that doesn’t go unnoticed when you can do those little things,” Murphy said. “Those are the things that excite me.”

In the seventh, with the game tied at 3-3, Perkins singled with two outs, stole second and took third on a wild pitch before Turang raced down the first base line on a swinging bunt single that gave the Brewers another lead.

Murphy used one of his favorite words to describe that kind of offense: Relentless.

“You do that over and over, you’re going to put yourself in position to win,” he said. “That’s why I’m proud of these guys, for playing this way.”

“We never give up,” Rea said. “We keep competing. We take anything we can get and take advantage of it.”