Halton's blast was the highlight of a five-run inning, after which the Brewers coasted to their fourth straight victory.
The home run by Halton, the seventh batter of the inning, came with two away off Chris Rusin (2-5).
Thornberg (3-1) walked two and struck out four while making his sixth start of the season and the ninth in his two years in the majors.
The Cubs dropped their fifth in a row and moved within one reaching 90 losses for the campaign.
Notable deaths of 2014 [PHOTOS]