The Brewers also swept the season series from San Francisco, winning all six matchups between the teams. They had not accomplished that feat since going 9-0 against the Marlins in 1998.
"[Lincecum] certainly deserves all the attention he's got because he's unbelievable," Braun said. "But Manny has been phenomenal for us. We've got [Ben] Sheets and [CC] Sabathia, our two-headed monster at the top of our rotation, but I think Manny has been our best pitcher. That's something to be said."
Braun and Corey Hart homered off Lincecum (11-3), who lost for the second time in three decisions after beginning the year 10-1. After Hart's second-inning solo home run put the Brewers on the board, Parra (9-2) chipped in with an RBI single over the shortstop and extended the hitting streak by Brewers pitchers to five games.
On the mound, he was even better in winning his eighth straight decision. He allowed only four hits in the first seven innings before the Giants rallied for three hits and two runs in the ninth, scoring both when Aaron Rowand's double popped in and out of Hart's glove as Hart retreated to deep right field.
Parra also set a career high with nine strikeouts.
"With what CC does and Ben, it ups the ante," said Parra, a California native who grew up a Giants fan and called pitching in San Francisco "a dream come true."
"It makes you kind of want to taste the same thing they are," Parra said, "and not have to use the bullpen. That's a goal now, to keep going deeper and deeper into games."
Lincecum took the loss after allowing five runs on six hits in six-plus innings. He struck out eight but walked four, and both Hart and Braun connected on two-strike pitches. Hart hit a homer leading off the second inning and Braun hit a three-run shot in the seventh that knocked Lincecum from the game.
Braun fouled off four consecutive two-strike offerings before hitting his team-best 24th home run this season. He added a two-run double in the ninth.
"[Lincecum] is absolutely filthy, nasty," Braun said. "I was just trying to put the ball in play, to be honest with you, trying not to swing at that splitter he kept throwing at me. I think he actually made a pretty good pitch -- a fastball in -- and fortunately I got to it."
Before Braun connected, Lincecum would bend but not break. The Brewers were 1-for-8 with runners in scoring position through six innings, the only hit being Parra's bloop RBI single.
In the three-game series, the Brewers scored 24 runs.
"We're really swinging the bats well," Brewers manager Ned Yost said. "Braun had great at-bats today. Prince [Fielder] had great at-bats. Really, really good, under control, solid swings. And Manny was excellent on the mound."
The Brewers swept a road series of more than two games for the first time since June 29-July 1, 2004, when they won three in a row at Colorado. This season, the Brewers are 24-26 on the road, and with Sunday's win, they moved to a season-high 12 games over .500 at 55-43.
"We're playing a lot better on the road," said Yost, whose club has traditionally struggled away from Miller Park. "We're past all that."
They packed up Sunday evening and headed to St. Louis, where the Brewers begin a key stretch of the schedule against National League Central rivals. They will have an extra man in the fold after completing a trade Sunday for Giants veteran infielder Ray Durham.
It was Milwaukee's second acquisition in as many weeks. The first was July 7 when Sabathia came over from Cleveland.
Count Yost among those trying to keep an even keel.
"The excitement gets you nowhere," Yost said. "Those players in our locker room understand that they're really, really good and they have the talent to do what we need to do. But they still have to go out and accomplish it, so [the trade talk] doesn't change anything from what we're trying to do. We have to prove our worth every single day."