The Brewers had been alone or tied for first place in the division every day since April 5, but a five-game losing streak had them tied with the St. Louis Cardinals coming into Monday's play.
Luis Valbuena added a solo homer for Chicago, while Jacob Turner (5-8) struck out seven over 6 1/3 solid innings to pick up the win, the Cubs' third in five games.
Back-to-back home runs by Khris Davis and Gerardo Parra in the seventh provided the only offense for the Brewers, who had starter Jimmy Nelson (2-6) allow three runs on nine hits over six frames.
UPI horse racing weekend preview
Bo Jackson: I can't help Jameis Winston anymore