Sexson hit his 36th homer of the season, a two-run shot in the first inning. The Brewers' slugger drove in four runs and has knocked in 100 this season, the third straight year in which he has reached the century mark.
After Sammy Sosa cut Milwaukee's lead to 2-1 with a sacrifice fly in the bottom of the first, Podsednik singled home Eddie Perez and Bill Hall in the second. He then stole second base, went to third on a wild pitch by Cubs starter Shawn Estes (7-11) and stole home.
Podsednik's steal was the Brewers' first theft of home since Mark Loretta did it in 1998.
Brewers starter Matt Kinney (10-9) won his third straight start, allowing five runs and seven hits in 5 1/3 innings.