Braun hit his NL-leading 29th homer and the Brewers connected four times Wednesday, beating the sloppy Houston Astros 13-4 to complete a three-game sweep.
The defending NL Central champions began the day 15 games behind first-place Cincinnati and 12 out in the wild-card standings.
"There's no reason to give up," Braun said. "Why are you going to give up, ever? I think until you're mathematically eliminated, you're going to continue to believe you have a chance. There's a lot of crazy things that have happened throughout the course of the history of this game."
Rickie Weeks and Cesar Izturis each homered in the fifth inning. Jonathan Lucroy added a two-run shot in the seventh, helping rookie Mike Fiers (5-4) win consecutive starts for the first time this season. The right-hander allowed two earned runs and eight hits in six innings to go with six strikeouts.
"It feels good when you get a lot of runs like that," Fiers said. "I'm not really worried about that too much. I'm just trying to do my job and put up zeros."
Milwaukee, which has won three straight after a 1-9 stretch, benefited from four Houston errors -- three within the first six Brewers batters. The Astros, who traded several veterans last month, lost for the 28th time in 31 games and own the worst record in the majors.
"They're still a major league team," Braun said. "A win is a win, and certainly a sweep is a sweep. It's not easy to sweep any team at this level, regardless of who they have or who they don't have."
Jordan Lyles (2-8) tied a career high by giving up seven earned runs in five innings. Winless in his last six starts, the right-hander also allowed nine hits and fell to 0-6 on the road this season.
"I've got to do a better job of limiting the big inning, which I've been terrible at this year," Lyles said.
Brett Wallace went deep twice for Houston, his first multihomer game.
Lyles unraveled in the fifth, when Milwaukee batted around. With the Brewers already leading 3-2, Nyjer Morgan and Carlos Gomez opened the inning with singles. After a double steal, Braun hit the next pitch for a two-run double to center.
Corey Hart added an RBI single and Weeks cracked his 12th homer to right-center. Izturis capped the rally with his second home run of the year for a 9-2 lead.
"We got some breaks today," Milwaukee manager Ron Roenicke said. "That inning we had two bloops, Corey kind of didn't hit his that good down the line, and Braunie hit a ground ball up the middle. We had four lucky hits in an inning, and that has not happened to us. So that was good. We haven't been getting the breaks."
Milwaukee, which beat Houston 10-1 on Tuesday, scored at least 10 runs in back-to-back games for the first time since May 4-5, 2010, against the Dodgers. ... The last time Lyles gave up seven earned runs was July 2 against Pittsburgh. ... Milwaukee has hit 22 homers and scored 68 runs in its last 10 games. ... Brewers LHP Manny Parra had his pitching shoulder examined after the game. The reliever has not pitched since July 24, and Roenicke said Parra will get his shoulder checked out again on Monday. Parra is not expected to pitch this weekend.