The Brewers, who avoided their longest skid at home in 14 years, had lost 11 of the past 13 overall, but the team was noticeably upbeat after a day off following a tough series in Minnesota, where they avoided a sweep Sunday.
"For us to be able to win a couple of games that are close will be key," said McGehee, who leads the National League with 40 RBIs. "Hopefully we can bottle that up."
Braun started it with a two-run homer in the first, and Weeks' two-run shot sealed it in the seventh.
In between, Wolf (4-4) was dominant after struggling through a miserable May. Milwaukee is still a franchise-worst 5-14 at home to start the year.
"We feel like we've been competitive the whole time, it's just kind of been bad luck here and there," Brewers right fielder Corey Hart said. "We're pretty upbeat for our record."
The Brewers heard another unfamiliar sound at home -- music in the clubhouse.
"I didn't know we had a stereo system," McGehee joked.
Houston starter Felipe Paulino (0-7) had his third quality start in his past four appearances, allowing only Braun's 447-foot blast over six innings.
The NL-worst Astros came in hitting a majors-low .227 with the fewest home runs, extra-base hits and RBIs in baseball, and they continued to struggle at the plate.
"We're not a good offensive team. Nobody's hitting, and until we do, what can you say but that," said Astros slugger Lance Berkman, who was 0-for-4 with two strikeouts.
Houston had four singles in seven innings off Wolf, who faced a bases-loaded jam in the second after two walks, and a two-on and two-out situation in the seventh. Both times, Wolf struck out the final batter to end the threat.
The veteran left-hander became the first Brewers starter to pitch at least seven innings since May 1. He was also one of the more unlikely candidates in recent weeks, going 1/3 with a 7.66 ERA in his first four May starts.
"Hopefully, this starts a trend," Wolf said. "As starters we know we need to do a better job."
Paulino allowed two runs over six innings, but the Astros gave a starter no run support for the 11th time this season to fall to 15-30 overall. They failed to score until Humberto Quintero's one-out double in the ninth.
"He gave us a chance to win. We didn't do much behind him to keep ourselves in the game, and it got out of hand there late," Berkman said.
Houston, which has spent all but five days alone in last place in the NL Central, also started 15-30 in 2005 before eventually reaching the World Series. That Houston club had ace pitchers Roger Clemens, Andy Pettitte and Roy Oswalt.
Oswalt, Berkman and Wandy Rodriguez are the only three players left from that team, but both Oswalt and Berkman have said they would be open to waiving their no-trade clauses to be dealt to contenders.
The Brewers hope they will be contenders, too, instead of dealing away top talent at the deadline despite being 18-27.
"We still feel like we've got a lot of wins in us," Hart said. "It's not too early, but we've got enough time where we can get on a roll."
Oswalt (2-6, 2.66 ERA) pitches for the first time Wednesday since news broke he requested to be traded. Oswalt has nine consecutive quality starts, but the Astros have given him just 2.29 runs in support per outing. ... Brewers bullpen coach Stan Kyles returned after prostate cancer surgery in April. ... Brewers manager Ken Macha was a bit testy after saying he's done answering questions about a recent vote of confidence he was given by owner Mark Attanasio and GM Doug Melvin. He shut down a TV reporter from asking a follow-up, telling him: "That's your last question of the day."