Scooter Gennett drove in two runs with a double, and Elian Herrera and Carlos Gomez each had RBIs to help the Brewers move 2 ½ games ahead of Pittsburgh and St. Louis. The Cardinals host San Diego on Thursday night.
Fiers (2-1) dominated and walked only one in his second start this season since being recalled from Triple-A Nashville to face the Dodgers last Saturday. In that one, he pitched eight strong innings and outdueled Zack Greinke for his first win this season.
Cubs starter Edwin Jackson (6-13) lasted just 4 2-3 innings and allowed five runs before being lifted for Jacob Turner, who pitched 2 1-3 scoreless innings in his Cubs debut. Jackson has lost six of his last seven decisions.
Chicago pinch-hitter Chris Valaika drove in two unearned runs in the seventh off Zach Duke, the first of three Milwaukee relievers.
The Brewers broke through after scoring just five runs in the previous three games in the series - and six in their last four contests - despite resting Ryan Braun, Aramis Ramirez and Jean Segura.
Braun was held out the lineup with a sore right hand. Brewers manager Ron Roenicke said Braun has been experiencing a flare-up of a nagging injury.
Roenicke said he noticed a difference in Braun's swing on Wednesday.
Anthony Rizzo had two of Chicago's five hits. After his first-inning double, Fiers retired nine Cubs in a row, including six strikeouts.
Gennett's double off the right field wall with two outs in the first drove in Jonathan Lucroy and Davis to put the Brewers ahead 2-0.
Davis lined his solo shot to left in the third to make it 3-0, then the Brewers added two runs in the fourth.
Reynolds hit his solo shot in the eight.
Brewers: RHP pitcher Kyle Lohse (11-7) could miss his next start with a right ankle "tweak" he picked up in an at-bat in Wednesday's 4-2 loss to the Cubs, but Roenicke won't make a decision for a few days. The Brewers have an off-day next Tuesday, making the adjustment to their rotation possible. "I'd hate to put him back out there again if that thing is still going to bother him," Roenicke said.
Cubs: OF Justin Ruggiano batted seventh and played right field. Ruggiano sat out Wednesday's game after leaving Tuesday night because of a groin strain.
Brewers: RHP Jimmy Nelson (2-3, 4.00) faces Dodgers RHP Zack Greinke (12-8, 2.84) at Los Angeles on Friday.
Cubs: LHP Travis Wood (7-9, 4.86) starts against New York Mets RHP Zack Wheeler (7-8, 3.53). Wood hasn't won since beating Philadelphia on June 15 and is on a four-game losing streak.