Parra allowed two hits in seven innings to win his sixth straight start and the Milwaukee Brewers beat Minnesota 5-1 on Saturday night to end the Twins' 10-game winning streak.
Bill Hall had a two-run double and Ryan Braun and Corey Hart also had RBIs for the Brewers, who have won nine of 12.
Jason Kubel hit a home run with two outs in the ninth for Minnesota.
"I think I've started to figure out that if you execute your pitches you're going to get outs," Parra said. "I don't have to have my best stuff to do well, as long as I'm going out there and being aggressive."
This time he did so against baseball's hottest team.
Parra (8-2), who has seven wins in his last eight starts dating to May 20, kept Minnesota hitters off balance all night. He struck out six, but walked four. He has allowed 14 free passes in his last three starts, including a career-high six in his last outing.
"The fastball against the lefties I kept missing with, but I made some pitches with my offspeed against them to get them out," he said. "Against the righties I basically used my fastball and split against them. I made some pitches when I had to. I don't like how I fell behind in counts, but I'm working through that."
Minnesota, which had just three runners advance to second base, grounded out 11 times against Parra, and did not hit the ball hard until the latter innings.
"You're seeing a young major league pitcher evolve into a pretty good major league pitcher," manager Ned Yost said. "He's been at the top of our prospect list for a long time and now he's gotten to the big leagues and is starting to feel comfortable and have some success."
At Spring Training, Parra was among a quartet of pitchers fighting for two spots on the Brewers roster. After making the team he went 1-2 in his first seven starts, with no outing longer than 5 1-3 innings.
Jason Kendall has had the best view of Parra's growth.
"He's getting more confidence every time he goes out and knows he's good," the Milwaukee catcher said. "He's not scared to go after guys. Behind in the count it's like 'Here it is,' and let's see what happens."
David Riske pitched a 1-2-3 eighth inning for Milwaukee and Mitch Stetter allowed Kubel's home run in the ninth.
Livan Hernandez (8-5) lost for the first time in three starts. After a rocky start, he went seven innings, allowing four earned runs and seven hits, throwing a season-high 115 pitches. He struck out five and snared a liner off the bat of Prince Fielder.
"He ate up some innings and protected our bullpen a little. That's huge after the fact. You don't like to get behind like that, but he sucked it up out there and gave us a chance," said manager Ron Gardenhire.
Milwaukee manufactured three runs on two hits in the third inning to go up 5-0.
A double by Hart scored one run, and after an intentional walk to Russell Branyan loaded the bases, Hall hit a first-pitch double of the right-field baggie to score two more.
Hernandez was visited by pitching coach Rick Anderson before walking Branyan. With former starter Boof Bonser warming up in the bullpen, Hernandez got Mike Cameron and Kendall to fly out with runners on second and third. Hernandez set down 14 of the next 16 Brewers.
Amid chants of "Let's Go Brewers" from the thousands of fans making the trip across state lines, Braun had an RBI single in the first and Cameron scored on a ground out in the second for a 2-0 lead.
"We just have to go out and win the series tomorrow and go from there," said Kubel, who homered for the second straight game and is tied with Justin Morneau for the team lead with 12. "You are not going to win every single game, so you just have to come back the next day and keep playing and keep doing what you were doing."