Gallardo (16-8) retired 14 consecutive Pirate batters en route to his eighth straight winning decision, allowing only two hits. The right-hander overcame four walks and struck out six.
Norichika Aoki put the Brewers ahead for good with a first-inning RBI single and added a sacrifice fly in the eighth to cap the scoring for Milwaukee, which came into the contest trailing St. Louis by 2 1/2 games for a National League wild card spot.
Jean Segura added a pair of run-scoring singles and while Carlos Gomez and Jonathan Lucroy each supplied three hits as the Brewers took the opener of a three-game set.
Pittsburgh's A.J. Burnett (15-8) was tagged with the loss, surrendering two runs on seven hits over six full frames.
Justin Bieber crashes Drake Bell's album release party
Putin thinks Obama would save him if he were drowning