''They put a nice comeback on him, had some good at-bats against him, but he finished it,'' manager Craig Counsell said of Hader.
Yelich's solo homer in the sixth inning was his 34th and tied the Dodgers' Cody Bellinger for the major league lead. It was Yelich's third home run in four games.
Trailing 5-0, the Braves rallied with two runs in the eighth on Josh Donaldson's two-run homer and two runs in the ninth on his two-run single.
Pinch-hitters Charlie Culberson and Johan Camargo led off the ninth with singles. With two outs, Freddie Freeman struck out on a pitch in the dirt, but reached first base after the ball got away from Manny Pina and Pina committed an error with his throw to first.
Donaldson hit a two-run single to make it 5-4 before Hader struck out Albies and earned his 21st save.
The Brewers jumped out to an early lead on Pina's two-run homer in the second inning. Yelich made it 3-0 in the sixth before Keston Hiura and Pina added RBI hits later in the inning to make it 5-0.
Milwaukee starter Chase Anderson (5-2) gave up only one hit, a double to Brian McCann in the second inning, in 5 2/3 innings. He walked three and struck out three.
''He's a decent player,'' Anderson said of Yelich, joking. ''When he goes into slumps, his slumps are hitting singles instead of homers or triples or doubles. So, to have a guy that's on your team to impact the game on a daily basis the way he does, it's huge.''
Dallas Keuchel allowed five runs, four earned, in 5 2/3 innings. After giving up the home run to Pina, Keuchel (3-3) retired 11 of the next 13 batters. But the Brewers got to him in the sixth, pushing the lead to 5-0 before he was pulled.
''I was kind of teetering on the edge there for a while and was fortunate to get to the sixth,'' Keuchel said. ''I felt like I didn't have too good of command of my fastball. I was behind on a lot of guys after the third and just couldn't corral it together there in the sixth. I just kind of ran out of gas and turned a close game into an extended vacation.''
Brewers: LHP Gio Gonzalez (arm fatigue), after two rehab starts, will start for Milwaukee on Saturday against the Diamondbacks in Arizona, Counsell said. RHP Adrian Houser moves to the bullpen. ... RHP Jimmy Nelson (elbow) will begin a rehab assignment at Class A Wisconsin on Sunday, Counsell said.
GETTING ON, STEALING BASE
Atlanta's Ronald Acuna Jr. reached base on a walk in the third inning, extending his career-best on-base streak to 23 consecutive games, the longest current streak in the majors. He then stole his 17th base of the season, after a review overturned an out call, exceeding his total of 16 in 2018.
Counsell joked that Gonzalez, who had had some travel problems, will double as the team's assistant traveling secretary. ''In addition to starting games for us, he will take on George Costanza's role,'' Counsell said.
KID CAN HIT
Hiura, the Brewers rookie, batted 8-for-11 in the series, including hitting two doubles on Wednesday.
Braves: RHP Julio Teheran (5-6, 3.71 ERA) will start at home against the Nationals' Stephen Strasburg (11-4, 3.46 ERA).
Brewers: Zach Davies (7-2, 2.89 ERA) faces the Diamondbacks' Merrill Kelly (7-9, 3.93 ERA) in Arizona.
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