The game went long, because Braun homered off Pirates closer Jason Grilli in the ninth inning for the second straight day. Grilli was saddled with another blown save, but this time Braun's blast only tied the game at 2. After the Brewers left the bases loaded in the 12th inning and stranded two more men in the 13th, Davis finally gave Milwaukee its first lead in the 14th.
Manager Ron Roenicke, fighting a cold and exhausted after using 23 of his 25 available players, let out a sigh of relief.
"It's great to win those games," Roenicke said. "They're really hard to lose. You throw everything you have out there."
Roenicke threw starter Marco Estrada plus six Brewers relievers -- who combined to allow only one Pirates run on an infield single in the eighth -- over eight strong innings. That relief crew combined to scatter seven Pittsburgh hits while striking out six, including two by winning pitcher Zach Duke and two more by Francisco Rodriguez during career save No. 311.
Rodriguez threw the game's final pitch long after the benches cleared in the third inning, when Carlos Gomez tripled and reacted to some sharp words from Pirates starter Gerrit Cole. Gomez, Brewers bench coach Jerry Narron and Pirates outfielder Travis Snider were all ejected, and they watched from their respective clubhouse as Milwaukee won the four-game series.
The Brewers still have baseball's best record at 14-5, but they now must worry about a suspension for their leadoff hitter and co-leader in home runs. After a similar incident against the Braves last September, Gomez drew a one-game suspension from Major League Baseball.
At least they could worry after a win.
"It's huge," Braun said. "At the end of the day, a win is a win and a loss is a loss, but there are certain games that feel like they're more meaningful than just a win or a loss. Obviously, emotions were running high with everything that went on during the game. Huge win for us."
The Brewers are 9-1 away from Miller Park, the National League's best road record to start a season since the 1995 Atlanta Braves started 10-0 away from home. Milwaukee has won six of seven matchups against the Pirates this season, including three of four in the just-completed series, all in comeback fashion.
"Great series. We could have easily been swept," Braun said. "We really could have -- and arguably should have -- lost each of the last three games, so to find a way to win all three of those games on the road is very encouraging moving forward."
Four hours and 21 minutes after the game began, the linescore looked like computer code, with the teams trading zeros and ones.
Neil Walker hit a long solo home run for the Pirates in the fourth inning and Mark Reynolds answered for the Brewers with a blast in the eighth. The Bucs came back with a manufactured run in the bottom of that inning before Braun struck against Grilli, drilling a home run to the left-field seats that handed the Pirates' usually-stout closer another blown save.
Grilli was glad to see the Brewers leave town on Sunday night. He had not allowed a Brewers run since 2007, when he pitched for the Tigers and Braun's big league career was all of three weeks old. Grilli had delivered 17 consecutive scoreless appearances against Milwaukee along the way, but that streak is now history.
"It was a breaking ball that was up in the zone," Pirates manager Clint Hurdle said. "First-pitch fastball called strike one, [then a] slide-step breaking ball he's executed many, many times, and the ball just never got where he wanted it to."
While Brewers relievers kept the Bucs at bay in extra innings, Milwaukee's hitters were similarly struggling. The Brewers stranded the bases loaded in the 12th inning against Justin Wilson and left two men on base in the 13th against Gomez, who walked Braun intentionally before inducing a Jonathan Lucroy popout.
But Davis struck leading off the 14th when Gomez hung a slider. He had three hits Sunday after going 2-for-24 in his previous seven games, including his first home run in 66 at-bats this season. Last year, Davis hit 11 homers in only 136 at-bats.
"It was hard to see with the shadow," said Davis. "Luckily, I got it. ... I'm not sure if I snapped out of it. I was just trying to go out there and do something small, really, and it turned into something big."
Give the Brewers' bullpen its due. Milwaukee's relief corps owns a 2.67 ERA (17 earned runs in 57 1/3 innings), all the more impressive considering the Pirates scored nine runs in the final two innings on Thursday.
"They keep doing it," Roenicke said. "I didn't know if we were going to ever score, but if they keep doing that long enough, they give somebody a chance to pop one."
"If we would have lost today's game, we still have a split in the series," said Duke, "but to take three out of four here really makes a statement that we're here to stay."