Parra (9-10) won for the fifth time in seven starts despite allowing six runs and 10 hits with four walks and two strikeouts in six innings.
"It doesn't matter (how I pitched), all that matters is we won," Parra said.
Parra has an 8.25 ERA in his last seven starts, but Milwaukee has averaged 7.1 runs in those games.
"We have a good offense, that's what it means," he said. "That's pitching with the offense that we've got.
"For my own personal satisfaction, I'd like to pitch better," said Parra, who has a 6.66 ERA this season. "But at the end of the day everyone in this clubhouse is happy when we win so that's all that matters."
Trevor Hoffman pitched the ninth for his 28th save and upped his all-time record total to 582.
Pittsburgh starter Zach Duke (10-12) was attempting to set a career high in wins, but had his shortest outing of the year, allowing seven runs and 11 hits in three innings.
"I wasn't good and for whatever reason I was out of whack and they were locked in," Duke said.
The Brewers have won 19 consecutive games over Pittsburgh at Miller Park, last losing to the Pirates in Milwaukee on May 3, 2007.
Pittsburgh rookie Andrew McCutchen went 3 for 5 with four RBIs. The center fielder had a single, double and home run to extend his hitting streak to 10 games, but missed hitting for the cycle when reliever Todd Coffey struck him out in the eighth.
"I didn't even know about the cycle until you just said something about it," McCutchen said when talking to reporters after the game. "We were down the whole time and that would be a selfish act if I was thinking about it."
Fielder hit a three-run homer in the first inning for the consecutive second game, but this time the Brewers held on for the win. Milwaukee scored four runs in the first inning Thursday but lost 8-5 to Cincinnati.
The first baseman hit a 1-1 pitch from Duke 448 feet into the stands in right-center. His 36th homer gave him a major-league leading 118 RBIs and gave Milwaukee a 3-0 lead.
Eight straight batters reached base in the inning, and consecutive RBI singles by Alcides Escobar and Parra made it 5-0 at the end of the first.
Bourgeois hit his first major league home run in the bottom of the inning to give Milwaukee a 6-2 lead.
Pittsburgh made it 6-4 in the third on Pearce's two-run double.
Escobar's RBI single gave Milwaukee a 7-4 lead in the bottom of the inning.
Braun hit his 28th home run in the fourth off Chris Bootcheck for an 8-5 lead.
McCutchen hit his 10th homer, a two-run shot and his third in four games, to bring the Pirates within 8-6 in the sixth. Parra finished the inning and was removed to start the seventh.
"I'm sure if you talk to him he's going to say, 'Well, I only had four mistakes and they didn't miss any of them," Milwaukee manager Ken Macha said of Parra. "Actually, when that happens those pitches are all under the microscope.
"You've got to look at the other side, how many good pitches he makes," he said. "But when you give up six runs, that's what he gave up in six innings, you've got to do better than that."
Pittsburgh manager John Russell and C Ryan Doumit had a closed door meeting after the game. Russell removed Doumit midway through the fifth inning and Doumit was not injured. "That's between Ryan and myself," Russell said. ... The Brewers' home winning streak over the Pirates is the longest since Baltimore beat Toronto 19 times at Memorial Stadium from 1978 to 1981. ... It was Duke's shortest outing since he lasted only 2 1/3 innings on July 6, 2008 in an 11-6 loss at Milwaukee, a span of 37 starts. ... The roof was closed in the fourth inning as stormy weather approached.