Parra demoted after Brewers loss
Contreras (2-5) struck out eight and walked two, using his array of arm angles and breaking pitches to frustrate the free-swinging Brewers.
Since returning from a monthlong demotion to the minors, Contreras has given up just three hits in 16 scoreless innings. He earned his first road win since May 14, 2008.
Highly touted prospect Gordon Beckham drove in his first two runs as a major leaguer and Paul Konerko also had two RBIs as the White Sox batted around in the second and scored as many runs in the inning as they have had in any game in June so far.
Ramon Castro also homered in the fifth.
The 37-year-old Contreras, who had faced one batter over the minimum through seven innings, finally began to tire in the eighth and loaded the bases by walking two around a single by Jason Kendall with two outs.
But to the delight of the large contingent of White Sox fans who made the 90-mile journey north this weekend for the first series between the teams in eight years, manager Ozzie Guillen left Contreras in.
Contreras retired Craig Counsell on a popup to end his day.
Pinch-hitter Casey McGehee's two-out single off Scott Linebrink in the ninth gave Milwaukee its lone run.
The White Sox improved to 5-9 in June after hammering Parra (3-8).
Konerko, who'd missed the previous two games with a nagging thumb injury, and Castro singled to start the second inning. Jayson Nix hit a ground-rule double to open scoring and Brian Anderson walked to load the bases.
Beckham, Chicago's first-round pick in the 2008 draft, hit a two-run double after a 2-for-28 start to his career. Parra got Contreras to pop out and Scott Podsednik to hit into a run-scoring groundout.
But the young left-hander walked Alexei Ramirez and Jermaine Dye to load the bases and Konerko singled in two runs in his second at-bat in the inning to make it 6-0, chasing Parra.
Parra's ERA has ballooned from 4.57 to 7.52 while losing four of his last five starts. Brewers general manager Doug Melvin said before the game he'd wait to see how Parra performed before considering a roster move, but with two of the next nine days off, the NL Central leaders won't need a fifth starter until June 28.
He obviously didn't wait long. Melvin had visited Parra in the clubhouse before the end of the game and he was immediately optioned to Triple-A Nashville for left-hander Chris Narveson.
NOTES: 3B Beckham fumbled a hard-hit ball by Corey Hart that was ruled a single in the third, and threw away Hart's grounder in the sixth for an error. ... Castro asked to keep the ball after his second-inning single. It was the 11-year veteran catcher's first hit as a member of an AL team. ... Brewers SS J.J. Hardy is hitless in his last 24 at-bats. ... The Brewers lost their 999th game as a member of the NL after switching leagues before the 1998 season. ... The Brewers will introduce RHP Eric Arnett, their first choice (26th overall) in the draft, in a news conference set for Sunday. Arnett had previously agreed to terms pending a physical.