The game was scoreless until the seventh, when Jordan Danks launched a two-run homer off Johnny Hellweg. The Sox were up 3-1 in the eighth, but Adam Weisenburger tied it with a two-run homer off Eric Surkamp.
Neither starting pitcher allowed a run. Milwaukee's Yovani Gallardo yielded two hits over 3 1/3 innings, while Chicago's Chris Sale, named the club's Opening Day starter earlier on Monday, allowed two hits and struck out three over 4 1/3 frames.
The White Sox threatened in the first, seemingly primed to take advantage of a poor showing by the Brewers' defense. Chicago had the bases loaded due in part to an error by third baseman Aramis Ramirez, playing in just his third game of the spring. That play was preceded by a long fly ball that hit off right fielder Sean Halton's glove, which was ruled a double.
But Gallardo yielded one hit through the remainder of his outing, exiting after coaxing a ground ball from Adam Dunn to begin the fourth.
"Things like that [errors] are going to happen in the regular season," Gallardo said. "There's not much I can do about it. I just have to keep making pitches. That was big for me to get out of that inning without allowing any runs. With second and third and one out -- just make pitches."
The Brewers weren't able to do much with Sale, who induced seven groundouts among the 15 batters he faced. The Brewers didn't have a baserunner get past first base until the sixth, when pinch-runner Kevin Mattison stole second.
Up next: The Brewers are off on Tuesday, one of two off-days they have this month. Play resumes on Wednesday in Tempe when the Brewers visit the Los Angeles Angels of Anaheim at 3:05 p.m. CT. Right-hander Matt Garza will take the mound against the Angels.
Alyson Footer is a national correspondent for MLB.com. Follow her on Twitter @alysonfooter. This story was not subject to the approval of Major League Baseball or its clubs.