The Cubs racked up five runs in the sixth inning to take control en route to their seventh win in eight games.
With the score tied 5-5, Milwaukee's bullpen fell apart with two hit batters and a two-run single by Soto.
Soto led off the fifth inning with his 11th home run of the season. Lee stroked a two-run double in the fourth.
Chicago added two more runs in the second, one of which strolled home from third when Chris Smith plunked Milton Bradley with the bases loaded.
Milwaukee starter Yovani Gallardo (12-12) took the loss after giving up seven runs on seven hits and five walks over 5 1/3 innings.
Corey Hart drove in three runs for the Brewers.
Aaron Heilman (3-3) picked up the win for pitching a scoreless sixth.
Copyright 2009 by United Press International.