CHICAGO -- The Milwaukee Brewers have used tidy pitching to sweep back squarely into the postseason picture.

Zach Davies tossed seven strong innings for his major league-leading 17th win and Travis Shaw launched a tiebreaking two-run homer in the sixth as the Brewers beat the Chicago Cubs 3-1 on Sunday.

The Brewers completed a three-game sweep of the defending World Series champions at Wrigley Field for the first time since May 2002. The win closed Milwaukee within two games of National League Central-leading Chicago.

The Brewers outscored the Cubs 20-3 in the series -- quite a turnaround after losing three straight in Cincinnati and being outscored 21-8 by the Reds.

"They pitched some good games," manager Craig Counsell said of his staff. "(Davies) was excellent today for sure ... doing it against hitters that are very familiar with him with the right combination of pitches."

Davies (17-8) allowed one run on seven hits while striking out six and walking one. The 24-year-old entered tied for the major league lead in wins with three big-name aces -- Clayton Kershaw, Zack Greinke and Chris Sale.

Davies' said he used "a good mix of everything" to keep Cubs' hitters off balance.

The right-hander, in his second full major league season, is 10-4 in his last 15 starts. His shutdown of Chicago left the Brewers on the Cubs' tails, rather than four games back.

"It's going to make September very interesting and fun to play for," Davies said. "I'm just trying to do my part at keeping the team in ballgames and letting the guys take care of the rest."

With the game, Shaw put the Brewers ahead 3-1 when he tagged Kyle Hendricks (6-5) for a towering drive that bounced off the message board in front of the party deck in right field and landed in the basket. It was Shaw's team-leading 29th homer and came against a strong wind blowing in from the east.

"Honestly that's about as good as I can hit a ball," Shaw said. "I thought it went too high. I thought the wind was going to knock it down. Luckily, it snuck all the way home."

After Anthony Swarzak pitched a 1-2-3 eight inning, Corey Knebel struck out the side in the ninth for his 34th save.

Stephen Vogt drove in the Brewers' first run with a groundout.

Rene Rivera had two hits and drove in the Cubs' lone run with a double.

Hendricks, locked in a duel with Davies until Shaw's homer, allowed three runs on four hits through six innings. The righty struck out seven and walked two.

"Kyle was outstanding today," manager Joe Maddon said. "We were just unable to string together any hits and our power has been negated a bit."

In their last eight games, the Cubs have scored 16 runs -- and eight of those came in a win at Pittsburgh last Thursday.

"We aren't hitting," Maddon said. "It's contagious to hit as well as it is contagious to not hit. You've got to just keep working your way through it."

The Cubs jumped ahead 1-0 in the second when Rivera's liner to right with two outs glanced off Hernan Perez's glove and Ian Happ raced home from second. It looked like Perez was lined up to catch the ball, but Rivera was awarded a double.

The Brewers tied it at 1 in the fourth without hitting the ball out of the infield. Ryan Braun, who led off with a bunt single, scored from third on Vogt's groundout to second.

Shaw's drive in the sixth put Milwaukee ahead for good.

NOTES: The Cubs activated C Willson Contreras from the disabled list on Sunday and he struck out swinging as pinch hitter in the seventh. Manager Joe Maddon plans to ease Contreras back into action this week. Contreras went on the DL on Aug. 11 after suffering a right hamstring strain at San Francisco on Aug. 9. In 42 games from June 19 until the injury, the 25-year-old hit .299 with 16 HR and 39 RBIs. ... Brewers manager Craig Counsell said he was shocked when he learned on Saturday that RHP Jimmy Nelson's right shoulder injury was season-ending. Nelson pitched five innings for his career-high 12th win on Friday in a 2-0 Milwaukee win, but jammed the shoulder diving back to first base after lining a single off the wall and rounding the bag. Initially, both Counsell and Nelson thought the injury wasn't serious, but tests showed it was a right rotator cuff strain and partial anterior labrum. "You thought you dodged a bullet," Counsell said.