Chacin (4-1) outdueled James Shields, who hasn't won a game since Opening Day despite pitching well recently. Shields (1-6) gave up three solo home runs but worked into the eighth inning.

Milwaukee's Jesus Aguilar, who finished with three hits and a walk, added a two-run shot off reliever Jace Fry in the eighth inning.

The Brewers, leaders of the National League Central, have won 12 of their last 16 games, and they avoided back-to-back losses for the first time since late April, when the Cubs swept them in four games at Wrigley Field.

The White Sox, who snapped a four-game losing streak in beating the Brewers 8-3 on Friday, have lost seven of their last nine games. They had only five hits on Saturday.

In the third inning, Erik Kratz, playing in only his third game in the majors this season since the Brewers acquired him last month as their backup catcher, took a low-and-in 79 mph breaking pitch from Shields and smacked it down the left-field line for his second homer and a 1-0 lead.

The White Sox came within inches of tying the game in the sixth.

Yoan Moncada led off with a single, and after a flyout, he stole second base. Jose Abreu then hit a ground ball that appeared ticketed for center field, but Brewers second baseman Jonathan Villar ranged far to the shortstop side of second to glove the ball and nab Abreu at first, while making Moncada stop at third.

The Brewers then brought in lefty reliever Josh Hader, a flame-throwing strikeout specialist, who whiffed right-handed pinch hitter Jose Rondon on three pitches to end the inning.

Minutes later, with one out in the top of the seventh, Villar laced the first pitch from Shields, another upper 70s breaking pitch but this one right down the middle, into the seats down the right-field line to expand the lead to 2-0. It was Villar's fourth home run of the season, and he also had three hits on the day.

In Chacin's 5 2/3 innings, he gave up three hits with one walk and five strikeouts. It was his first win since May 10.

Hader struck out three in 1 1/3 innings, and right-hander Taylor Williams pitched the final two innings, preserving the shutout despite allowing a single and a double to start the ninth.

Shields exited in the eighth after giving up a home run to the first batter, Lorenzo Cain (seventh of the season). It was Shields' fourth straight start of going at least seven innings and giving up three or fewer runs, but he has two losses and two no-decisions in that span.

Fry entered and immediately walked Yelich before surrendering the two-run shot to right-center field to Aguilar, his 10th of the season.

--Field Level Media