Between those outings, Hart pushed the Brewers ahead. His fly ball to straightaway center field off hard-throwing Cardinals reliever Jason Motte (2-2) nearly went for a grand slam.
"Man, that was huge," said Parra of the Brewers' win, only their second on what was a tough, seven-game road trip to Florida and St. Louis. "The job that Corey did to make sure he got that ball deep, that wasn't an easy pitch to do it on. ... And the other thing is that so much has been said about our pitching staff, and for the bullpen to come in and pick us up like that was huge. They did a great job, and they've been worked hard."
Braddock was on the receiving end of a beer shower, the Brewers' traditional celebration for career milestones. He also got something more permanent in a game ball.
"It's a great experience, especially coming at this time," Braddock said. "The team has been fighting hard every night. I was fortunate to have my win fall on a night that was [a team effort]."
In the early innings, it looked like the Brewers would have little need for that over-worked bullpen. Parra, who was just re-inserted to the starting rotation on Thursday, became the first Brewers pitcher ever to strike out four batters in a single inning -- the fourth -- and had a career-high 10 strikeouts by the end of the fifth.
In the fourth inning, Parra had already recorded the first two outs via strikeout before Cardinals catcher Yadier Molina swung at a third strike in the dirt that got past catcher George Kottaras. Molina reached safely on the wild pitch, but Parra recovered to strike out Colby Rasmus to end the inning.
Parra is the second Major Leaguer to post a rare four-strikeout inning this season. The Mariners' Felix Hernandez did it on Thursday against the Twins.
"The key was that I was commanding my fastball, and I was throwing all of my offspeed [pitches] for strikes, too," Parra said. "Even [if] you do that, and you expand, they can't just shut it down. George did a great job. I didn't shake him off more than one time."
Things came apart suddenly in the sixth inning. Parra surrendered a home run to Albert Pujols that cut Milwaukee's lead to 3-2, then walked three batters in a row with one out to prompt an unlikely call to the bullpen.
In trotted Dave Bush, who was originally slated to start Sunday before the Brewers surprised everyone by tabbing Parra. Bush had not appeared in relief all season, and here he was inheriting a bases-loaded, one-out jam with a one-run lead on the verge of getting away.
"I knew there was a chance I could pitch," Bush said. "But I wasn't necessarily expecting that."
The Cardinals countered with left-handed-hitting pinch-hitter Skip Schumaker. Brewers manager Ken Macha saw that move coming, but was not ready to burn the bullpen's only left-hander, Braddock, at that time, so his other choice was right-hander Kameron Loe.
Macha explained the call for Bush.
"We needed a strikeout, and I thought that Bush's stuff against either [Aaron Miles, who was originally scheduled to bat] or Schumaker had a better chance," Macha said. "Loe, to me, his Major League history is that left-handers hit him pretty well. He's done well so far, but ... I felt comfortable with Bush throwing his curveball to the left-hander and getting him out."
Schumaker lasted 12 pitches before striking out. He fouled off seven pitches, six of them with two strikes, before swinging and missing on an inside fastball.
"Some good pitches, and he kept fouling them off and fouling them off," Bush said. "I pulled the last one a little bit. It wasn't quite where I wanted it, but I had thrown a bunch of strikes in a row and he was ready to swing. That probably worked to my advantage more than anything else."
That prompted another bullpen call for Loe, who retired another pinch-hitter, right-handed hitter David Freese, on a fielder's choice grounder. The out preserved Milwaukee's one-run lead.
What happened to Parra?
"I ran out of gas," he said. "Everything was up. I was doing a good job of hitting my spots with my fastball earlier in the game, but there at the end, everything was up. I started yanking some balls, and that was a sign.
"Unfortunately, we had to get the bullpen in there. I expected to get through that inning."
Loe worked a scoreless seventh, but allowed a run in the eighth that tied the game at 3. Hart won it in the 10th inning and was one of three Brewers to drive in a run; second baseman Rickie Weeks scored twice and hit his 10th home run this season, and Casey McGehee drove in a run in Milwaukee's two-run first inning against Cardinals starter Jaime Garcia, who entered the night with the second-best ERA in the National League.
At least for the first five innings, Parra was better.
"That was the best I'd seen him, probably the best we had all seen him," Cardinals shortstop Brendan Ryan said. "He had command of three pitches and was throwing hard. He was mowing us down. That was pretty impressive."