MILWAUKEE -- In each of the first two games of their four-game weekend showdown at Miller Park, the Milwaukee Brewers and Chicago Cubs went into the 10th inning before the defending World Series champions broke their young challengers' hearts.

So Saturday afternoon, when the Cubs again manufactured a go-ahead run in the top of the 10th inning, the few remaining local fans among the sold out crowd of 44,067 prepared for more agony.

Instead, the Brewers flipped the script, getting a one-out double from Ryan Braun that set up a two-run walk-off home run from Travis Shaw as Milwaukee rallied late -- and kept its slim postseason hopes alive -- with a 4-3 victory.

"I haven't been able to come up with the words for this series," said Brewers manager Craig Counsell, whose team got within 4 1/2 games of the Cubs and one of the Rockies for a wild-card spot. "If this hasn't been the best series that you've seen in a long time this is about as exciting as it gets. It is as exciting as it gets. They're clearly coming into a good place where they're really tough to beat but we hung with them today."

Shaw hit his 31st homer after Milwaukee tied it in the ninth on a homer by Orlando Arcia off Wade Davis. The Cubs, who won the first two games in the 10th, took a one-run lead on a single by Jon Jay before Milwaukee dramatically won it.

Davis came back out for the 10th, working two innings for the second time in three games. He struck out Neil Walker to open the inning but Braun sent a double down the line and into the corner to bring up Shaw, who took ball one before connecting on a hanging curveball to win it.

"He missed with the curveball on the first pitch, and I was going to see if he'd do it again and he tried it again," Shaw said. "Last night I missed an opportunity early in the game to kind of blow it open. It just feels good to come out on the right side of things after a couple of tough days."

Davis (4-2), working multiple innings for the second time in three games, hadn't blown a save since Sept. 2, 2016.

"My arm was dragging a little bit," Davis said. "I just made a lot of bad pitches and good pitches for them to hit."

In the ninth, Davis struck out Neil Walker to open the inning but missed his mark coming inside on a 0-1 fastball that Arcia ripped down the left-field line for his 14th home run of the season, tying the game 3-3.

"Just wanted to get it in more and obviously I didn't," Davis said. "He put a pretty good swing on it."

Davis hadn't allowed a home run since Aug. 13 but recovered quickly from there, retiring the next two batters and Chicago got to work quickly in the 10th against Jeremy Jeffress (4-2) with Ian Happ starting things off by drawing a leadoff walk.

Jason Heyward moved him over with a sacrifice bunt and Jay sent him home with a single back up the middle, putting the Cubs ahead. Jay stole second and took third on a throwing error by Stephen Vogt and, with the Cubs threatening to break the game open, Jeffress intentionally walked Anthony Rizzo, Chicago's leader with 32 home runs and 107 RBIs.

The move paid off as Jeffress got Wilson Contreras -- no slouch himself with 21 homers and 73 RBIs this season -- to bounce into a force, ending the inning.

"The walk hurt JJ today but again, he did a pretty good job," Counsell said. "It's not hard contact that's beating him. It was just a roller up the middle."

Milwaukee got a solid start from left-hander Brent Suter, who held the Cubs to a run on six hits with a pair of strikeouts over 5 1/3 innings.

Kyle Hendricks was just as stingy, allowing just a run on Eric Thames' first-inning RBI single, despite giving up eight hits with a walk while striking out six over six innings of work.

The bullpens took over from there and maintained the tie into the eighth when Jacob Barnes, back out for his second inning, allowed a leadoff double to Ian Happ and a single to Heyward.

Counsell turned to setup man Anthony Swarzak to get out of the jam but Jay moved the runners over with a sacrifice bunt and Kris Bryant put the Cubs ahead with a sacrifice fly to center before Swarzak ended the inning.

NOTES: Chicago Cubs Manager Joe Maddon says he plans to keep his rotation in order this week, with LHP Jon Lester kicking off a four-game series at St. Louis on Monday despite command problems in his last outing. ... Milwaukee Brewers C Manny Pina missed a second consecutive game because of a sprained left thumb suffered Thursday in the series opener. ... The Brewers and Cubs have split the season series, winning nine games each, and wrap it up Sunday afternoon with Chicago LHP Jose Quintana (6-3, 3.95 ERA) facing Milwaukee RHP Chase Anderson (11-3, 2.74).