Prince Fielder, Mark Kotsay and George Kottaras also homered for Milwaukee, which began the night with a 5 1/2-game lead over St. Louis in the National League Central. The Brewers have not won a division crown since 1982, when they were in the American League.
Since joining the NL in 1998, Milwaukee has won no more than 90 games in a single season. The Brewers need two more victories this year to match that total, which was achieved in 2008.
Fielder's 33rd home run of the season tied it at 1-1 in the second. Kotsay hit a two-run blast in the third and Braun followed in the same inning with his first of the game. Kottaras contributed his solo shot in the seventh and Braun produced his 30th of the year in the eighth.
Joey Votto drove in all three Cincinnati runs with a pair of singles in the first and eighth.
Bronson Arroyo (8-12) gave up the first four Milwaukee homers and only one other hit in 6 1/3 while suffering the loss.
2014: The Year in Music [PHOTOS]