Most of Greinke's success this season has occurred at home, where he's 4-0 with a 1.08 ERA. He entered Friday with a 3-2 record and a 4.96 ERA away from Miller Park, and was facing the reigning American League Pitcher of the Month in Chris Sale.
"I definitely knew whoever was going to score a run, it was going to be the difference in the game," said White Sox shortstop Alexei Ramirez. "It was unfortunate it wasn't us."
Greinke (8-2) redeemed himself from a season-high 11 hits he allowed in his most recent start at Minnesota by holding the White Sox hitless through four innings.
He had to be flawless against Sale, who held the White Sox scoreless through eight innings.
"It's an exciting game to watch two pitchers battle like that," said closer John Axford, who pitched a scoreless 10th for his 13th save. "You're paying attention the whole time you're out there in the 'pen."
The Brewers registered just four hits off Sale. Reliever Addison Reed pitched a scoreless ninth before Aramis Ramirez led off the 10th against reliever Jesse Crain (1-1) with his second double of the game, increasing his hitting streak to six games.
Nyjer Morgan, who entered as a pinch-runner for Ramirez, took third on a wild pitch and scored on Weeks' single to give the Brewers their first win in extra innings on the road this season.
Manager Ron Roenicke said Morgan reaching third may have been the difference in the game.
"That ends up being a huge play, because if they don't have the infield in there, that ball may not go through," Roenicke said.
Weeks' batting average is still .186, but he's hitting .385 with a double, triple and four RBIs during his last six games.
"I'm coming to the field working hard every day," Weeks said. "I feel good right now. You've got to go out there and play baseball and keep swinging it."
Greinke was at 100 pitches after nine innings, when Roenicke decided to pull him for Axford.
Greinke said he could have thrown another inning, but it's probably better that he didn't.
"I felt like I could have went out easy," Greinke said. "But the last two guys I remember doing 10 innings both got hurt right after. I didn't want to take a chance with that, even though I felt good. I'm sure they felt good going out there, too."
Axford, who had blown three of his past five save opportunities, walked Gordon Beckham to start the 10th inning. He then struck out Adam Dunn and forced Paul Konerko to ground into the fourth double play of the night to end the game.
"When the balls were hit pretty good, it was right where we were playing most of the time," Greinke said.
White Sox right fielder Alex Rios singled for the first hit off Greinke in the fifth. A.J. Pierzynski then lined out right to Corey Hart, who tagged first with his glove to double off Rios for the first double play.
Greinke would go on to induce inning-ending double plays in the seventh and eighth innings on two grounders. He faced just 28 batters through nine innings.
"I think there were two balls squared up against him -- the base hit by Rios and the line drive to Corey at first base," Roenicke said. "The other two base hits went in, but that was really good. Great curveball today. He usually throws a curveball but not as good a bite and down in the zone like that."
The Brewers registered a hit off Sale in four of his eight innings, but never recorded a multi-hit inning off the starter. Weeks was stranded at third base after doubling in the fifth inning, when Sale struck out the side.
"Sale is really good," Roenicke said. "I see why his record and his ERA is where they are. He's really funky, along with great stuff."