MILWAUKEE -- The 2019 Brewers waited until the seventh inning of their 96th game to hit their first grand slam, and of course it was Christian Yelich who did it.

Yelich’s slam capped a six-run outburst in a 13-1 win over the Braves at Miller Park on Tuesday that had contributions from all corners of the lineup card -- all after president of baseball operations David Stearns said the team’s play over the two weeks leading to the July 31 Trade Deadline would help dictate whether he fortifies the roster.

• Box score

The Brewers’ most lopsided victory this season was just their third in 11 games, but that only scratched the surface of how badly they needed a night like this. They had not won a game by more than two runs in more than a month, since a 6-3 win in 14 innings on June 12 in Houston. They had not won by more than three runs since five days before that against the Pirates at home, which was also the last time Milwaukee managed to score in double digits.

“It was nice to be on that side of one of those games,” Yelich said. “I think we needed it. There was a lot of frustration, obviously, over the last few weeks or so. We definitely needed that one.”

Can one game make a lasting difference?

“It doesn’t hurt,” Yelich said.

Tuesday was the ultimate team effort. Brandon Woodruff had already pitched 6 2/3 quality innings in his first start since appearing in his first All-Star Game, and seven Brewers batters already had a hit before Yelich connected against Braves right-hander Huascar Ynoa with the bases loaded and two down in the seventh. The Brewers entered the day with the Cardinals and Indians as the only teams in MLB without a grand slam. With Yelich’s 33rd home run, it was down to the Cardinals and Indians.

Dodgers slugger Cody Bellinger also hit a home run on Tuesday -- No. 34 -- so Yelich remained one back in what is shaping into a fantastic chase for the home run crown. The two have homered on the same day 10 times this season.

Yelich also walked twice and scored three runs to pace a balanced offensive attack. Rookie Keston Hiura homered in his first at-bat Tuesday after finishing a home run shy of the cycle the night before, and finished with three hits, three runs scored and two RBIs.

Mike Moustakas tallied his 999th and 1,000th career hits. Ben Gamel hit a pair of RBI singles. Yasmani Grandal knocked an RBI single after imploring his teammates to “just play” the night before.

Lorenzo Cain, healthy again after dealing with a painful thumb injury for months, homered in the sixth after legging out a hustle double in the third inning and pumping his arm so hard that his helmet popped off.

“We’re looking to celebrate things, for sure. We just haven’t had much to celebrate,” manager Craig Counsell said.

“We know how important these games are,” said Woodruff, who saw the Brewers improve to 15-4 when he takes the mound. “We’re trying to put it all together. ... Hopefully tonight is the start of a good run.”

For all of the hitting, Counsell had two defensive plays and one baserunning play circled on his scorecard. All were in the fifth, when third baseman Moustakas and shortstop Tyler Saladino made consecutive highlight-reel plays to get Woodruff through an inning that began with a Tyler Flowers homer for Atlanta’s only run, and when Yelich stole third before scampering home on a wild pitch to answer the Braves' tally. Flowers didn’t have to go far up the line to retrieve the baseball, and when he dived he nearly tagged Yelich.

“The game really swung, to me, in the fifth inning,” Counsell said. “That’s a probably 2-3 run swing, and the game is really different if we don’t make those plays.”

“You just have to go right off the bat,” Yelich said. “You have to trust your instincts and your initial read. You can hesitate when you do something like that. I actually thought he was going to get me.”

But he didn’t. It was a rare night in which everything went right.

“We’re capable of doing that -- playing in all three phases of the game,” Yelich said. “The good thing is, as bad as we’ve played the last 3-4 weeks, we’re still right there. We really are. We’ve been fortunate to where we’re right in the middle of the race, not in a terrible spot. We’re very fortunate, and if we get things back going like the way we’re capable of, we’ll be all right.”