They got help from starting pitcher Mark Buehrle, who hit his first career home run, and from their usual designated hitter Jim Thome, who twice showed bunt in a pinch-hit appearance before drawing a one-out walk in the top of the ninth.
And, finally, from Clayton Richard, a member of the starting rotation who pinch-ran for Thome and scored the game-winning run on a two-out single by A.J. Pierzynski.
"I enjoy it because you feel like you're part of the game when you're managing," White Sox skipper Ozzie Guillen said of Interleague Play. "You have to be careful about what kind of move you're going to make and when you make it. You just get to the point where you can make more mistakes in the strategy and stuff in the National League."
Guillen and the White Sox pushed all the right strategic buttons on Sunday. Guillen opted to pinch-run Richard to save Jermaine Dye and backup catcher Ramon Castro on the bench. It was the first time Richard said he'd ever been called upon to pinch-run, but Guillen said he did what he had to do.
"Anybody who pinch-ran was going to be faster than [Thome]," Guillen said. "I was kind of -- not nervous or worried, but concerned that this kid was going to get hurt running the bases, but I had to do what I had to do."
Then there was Pierzynski making an odd decision, with two outs and runners on first and second, swinging on a 3-0 pitch from Brewers closer Trevor Hoffman to hit the go-ahead single.
"It wasn't a horrible pitch, I just knew that it was probably the best pitch I was going to get, so I just tried to stay up the middle," Pierzynski said, adding it was just one of a handful of times he's swung on a 3-0 pitch in his career. "He was trying to paint the outside corner low and away, and [Hoffman's] got such great control, it's tough."
Pierzynski's RBI was the first run given up by Hoffman this season, snapping a streak of 18 scoreless innings.
White Sox closer Bobby Jenks allowed one hit in the ninth inning to pick up his 14th save, while Hoffman was saddled with his first loss of the year. Reliever Matt Thornton earned the win in relief, coming in and getting the last two outs in the eighth inning.
Buehrle took a no-decision in the start, allowing four runs on seven hits, including three home runs. Though he hit his first career home run earlier in the game -- becoming the first White Sox pitcher to homer since Jon Garland did so against Cincinnati on June 18, 2006 -- he gave up a home run to the Brewers' Casey McGehee, the first of his career, and two others to right fielder Corey Hart.
"I looked up [at the scoreboard] in the fifth inning and it said I had 94 pitches, and that surprised me a bit," said Buehrle, who allowed three home runs for the first time since September 2006. "I was falling behind in the count a lot, and I had to come after those guys. Corey Hart's a great hitter, and when you fall behind 3-1 every time and he knows what's coming, it's kind of hard to keep him in the park."
The various moves were a result of various issues facing the White Sox. With Interleague Play continuing the next six games, they'll travel to Chicago's Wrigley Field and Cincinnati's Great American Ball Park without Thome's bat in their lineup. And the right thumb of Paul Konerko, while healthy the past two days, could once again flare up.
In fact, Sunday's craziness may turn out to be normal for the White Sox in the next six games.
"We're so banged up right now, and that's not an excuse, but anytime you're missing [key players], it's tough," Pierzynski said. "But you have to find a way to get through it, and we played a good game here. We made some pitches when we had to, got some hits when we had to and it was a good win."
Cash Kruth is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.