Hoerner drove in Javier Baez with one of his three hits, a two-out single off reliever Sean Doolittle to complete Chicago's rally from a 2-0 deficit.
Rex Brothers struck out all three batters he faced in the sixth for the win, the first three of eight strikeouts compiled by five Cubs relievers over five innings.
Craig Kimbrel pitched out of trouble in the ninth for his fifth save.
Baez and Cincinnati reliever Amir Garrett exchanged words in the eighth. Both benches and bullpens emptied, but no punches were thrown and there were no ejections.