Cubs back-up catcher and first baseman PJ Higgins touched closer Josh Hader for a go-ahead two-out double in the top of the ninth inning Wednesday afternoon.
That boosted Chicago to a 2-1 victory and a series win over the Brewers.
The Cubs have won four series in a row but they are still 12 games out of first place. Hader took his second loss while blowing a save for the second time.
Milwaukee lost even though starter Corbin Burnes was dominant while pitching seven scoreless innings and striking out 10 batters.
Keston Hiura hit his eighth home run of the season and made a spectacular catch in left field for the Brewers.
The team takes Thursday off, then welcomes Pittsburgh for a weekend series.