"Obviously this game doesn't count, but it feels good to go out there and pitch well and hit well," Lucroy said. "Hopefully, we can carry this over into Monday."
The Brewers stay home to host the Rockies beginning Monday. The White Sox will also open Monday at home against the Royals.
"You always look forward to the start of the season," White Sox manager Robin Ventura said. "It's just nice to get through it. Everybody's feeling good and healthy."
Before the Brewers' decisive rally, Rickie Weeks hit a two-run home run for the Brewers and Adam Dunn hit a solo shot for the White Sox before Chicago benefited from some sloppy Brewers defense, using two fifth-inning errors to score three go-ahead runs.
Alexei Ramirez, Gordon Beckham and Brandon Short all doubled off Brewers reliever Tom Gorzelanny in the fifth inning as Chicago turned a 2-1 deficit into a 4-2 lead. Two of the runs were unearned after errors charged to shortstop Jean Segura and second baseman Hainley Statia. Beckham, Short and DeWayne Wise drove in a run apiece in the inning.
The Brewers featured five big-league relievers for an inning apiece before the originally scheduled starter, Chris Narveson, worked a scoreless sixth. It was an opportunity for Narveson to adjust to the long relief role he will fill at the start of the season.
White Sox starter Gavin Floyd surrendered Weeks' two-run homer in the bottom of the first inning, but only one of the runs were earned because Brewers leadoff man Norichika Aoki had reached on an error. Floyd worked that lone inning and surrendered two hits, with a walk and two strikeouts.
Now both teams are ready to play for real.
"I think going into the season with a nice win is always good," Brewers manager Ron Roenicke said.
Up next: Chris Sale will take the mound, looking to build on a strong 2012, when he went 17-8 with a 3.05 ERA in 30 games, on Opening Day vs. Kansas City at 3:10 p.m. CT on Monday. Sale is 3-3 with a 3.12 ERA in six starts against the Royals.
Adam McCalvy is a reporter for MLB.com. Read his blog, Brew Beat, and follow him on Twitter at @AdamMcCalvy. This story was not subject to the approval of Major League Baseball or its clubs.