Braun homered off Grilli for a second consecutive game, hitting a tying shot in the ninth and sending the Milwaukee Brewers toward a 3-2, 14-inning win Sunday.
Khris Davis hit the go-ahead homer in the 14th, long after the Brewers and Pittsburgh got into a punch-filled brawl.
Both of Braun's homers ruined save opportunities for Grilli, an All-Star last season.
"It is the first time in two years-plus that he's had back-to-back bad marks," Pirates manager Clint Hurdle said. "This is going to show where everybody is with Grilli. Do his teammates and fans jump off the boat or not?"
Grilli has blown three of seven save opportunities this season. He converted his first 25 save opportunities last season.
It was Braun's 26th career home run against the Pirates, tied with the Houston Astros for his most against a single opponent.
Davis hit a solo shot off Jeanmar Gomez (0-1).
There had already been plenty of big blows before that deciding homer.
Brewers center fielder Carlos Gomez, Pirates outfielder Travis Snider, who played at Jackson High School, and Milwaukee bench coach Jerry Narron were ejected after a shouting match quickly escalated in the third inning.
The problems started when Gomez paused at the plate and flipped his bat to watch his two-out drive off Pirates starter Gerrit Cole.
Gomez said he thought the ball would be caught. Instead, it hit the wall and he sped into third base, making a headfirst slide for a triple.
Cole, who was near third base backing up the play, stormed toward Gomez and they exchanged words.
Cole said he told Gomez: "If you're going to hit it out of the ballpark, then you can stop and look at it. But it you're going to hit just a fly ball to center field, then don't stand and look at it.'"
That didn't sit well with Gomez. He took a couple steps toward Cole and the benches and bullpens emptied.
"Everything had stopped," Gomez said. "He told me something, I told him back, then I talked to the umpire. Then Snider came like a superhero, trying to throw punches at everybody. I just tried to protect myself."
Snider, who wasn't in the game, and Gomez shoved each other, and the Brewers star fell to the ground.
Milwaukee's Martin Maldonado came from the dugout and threw a punch that knocked off Snider's hat.
Pirates catcher Russell Martin called Maldonado's swing a dirty one and had to be restrained by teammate Gaby Sanchez as he walked off the field.
"I've never sucker punched anyone in my life, so I don't know what was running through his mind there," Martin said. "But I have been sucker punched, and I know after having that happen to me that I would never do it to anyone else."
The Brewers won their third in a row. Pittsburgh has lost three in a row and five of six.
Hurdle said the incident likely won't have any impact on the Pirates moving forward.
"You're not going to get any badges of honor for what happened today," he said. "You just try to move on after it happens and win the game. As far as galvanizing, all this does is provide tangible evidence to anybody who didn't think we were galvanized."
Zach Duke (1-0) pitched two scoreless innings and Francisco Rodriguez got his seventh save.
Cole allowed one run and six hits in a career-high eight innings, striking out six.
Cole appeared to be in line for the win after Jose Tabata's eighth-inning infield single scored Ike Davis to give the Pirates a 2-1 lead. Brewers manager Ron Roenicke challenged the call, but the play was upheld.
Braun hit his sixth homer with one out in the ninth off Grilli.
Mark Reynolds hit his fifth home run, a solo drive in the Milwaukee seventh.
Neil Walker homered for the Pirates in the fourth off Marco Estrada.
NOTES: C Chris Stewart went 1 for 6 in his Pirates debut. He missed the start of the season after undergoing arthroscopic right knee surgery last month. ... LHP Francisco Liriano (0-3, 3.96) is scheduled to pitch for the Pirates on Monday night at home against the Cincinnati Reds.
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