MILWAUKEE -- Earlier in the day, Brewers manager Craig Counsell said his team had to find a way to make more plays in order to claw out of its midseason slump.
Milwaukee then went out and did it Tuesday night.
"We talked about (making plays) a lot," Counsell said. "(We had) a lot of people doing a good job tonight."
Brandon Woodruff (11-3) gave up one run and five hits in 6 2/3 innings for the Brewers, who had lost eight of their previous 10 games. The right-hander walked one and struck out seven, snapping a 12-game streak in which Milwaukee starters failed to get a win.
With the Brewers leading 7-1 in the seventh, Yelich hit his 33rd home run of the season with the bases loaded. The shot, which came against Braves reliever Huascar Ynoa, was the first grand slam for Milwaukee this season and the second of Yelich's career. He also had one last Sept. 2 at Washington.
Mike Moustakas picked up his 1,000th career hit with a single to right-center field in the seventh. Braves first baseman Freddie Freeman stepped away from Moustakas to allow the 10-year veteran to acknowledge the standing ovation from the crowd of 31,599.
"Obviously, the most important thing was getting the W," Moustakas said. "Every one (win) counts right now. We haven't been playing our best baseball. Huge win for us. The boys came out and played phenomenal today."
Bryse Wilson (1-1) allowed four runs and six hits in four innings for the Braves. Wilson, recalled earlier in the day from Triple-A Gwinnett, became the youngest pitcher to start a game in the National League this season at 21 years, 208 days.
"His secondary stuff was just so-so tonight but he kept it manageable," Braves manager Brian Snitker said of Wilson. "We still had a chance coming out of the fifth, we were still within striking distance but it just kind of got out of hand."
Tyler Flowers scored the lone run for the Braves on a solo homer in the fifth, his eighth of the season. The 12-run loss is the largest deficit for Atlanta this year.
Wilson retired eight of the first nine batters he faced, allowing only a solo home run to Hiura in the second. But then four straight batters reached base, with Cain and Yelich coming around to score, and the flood gates opened shortly thereafter.
After finishing a home run short of the cycle on Monday, Hiura continued his hot streak at the plate. The home run extended his hitting streak to six games and he reached base a career-high five times.
"Obviously, it was nice to have the offense rolling like it was tonight," Moustakas said. "Keston's six for his last seven or something. He's just ripping the cover off the ball."
Yasmani Grandal had an RBI single and Moustakas a run-scoring double to push the Brewers' lead to 3-0 in the third.
Yelich scored on a wild pitch in the fifth and Cain homered in the sixth to make it 5-1.
Yelich's homer capped a six-run seventh inning that stretched the advantage to 11-1. Ben Gamel's RBI single and Cain's bases-loaded walk capped the scoring in the eighth.
STAYING ON BASE
Ronald Acuna Jr. reached base on a single in the third, extending his career-best on-base streak to 22 consecutive games. That ties Kansas City's Whit Merrifield for the longest active streak in the majors.
Braves: LHP Max Fried was placed on the 10-day injured list with a blister on his left index finger. Snitker says the blister developed during the fourth inning Monday night. Snitker pulled Fried after he pitched five scoreless innings.
Keith Jenkins can be reached at https://twitter.com/MrKeithJenkins
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