Zack Cozart and Scott Rolen also hit homers for the Reds, who entered the day with a half-game lead over Pittsburgh.

Milwaukee's Ryan Braun recorded his 1,000th career hit with a single up the middle in the fourth, becoming the 11th player in franchise history to reach the mark.

Bailey (9-6) allowed one run on six hits over eight innings to earn his first win in 11 starts against the Brewers. He had been 0-5 with a 6.50 ERA against Milwaukee, including a pair of ugly outings in losses this season. Norichika Aoki broke up the shutout with an RBI double with two outs in the eighth.

Aroldis Chapman struck out two in a perfect ninth for his 16th save. Chapman has 23 strikeouts in his last nine innings.

Cozart opened the scoring by lining a solo shot just over the left-field fence in the fourth inning for his 10th home run of the season. It marked the Reds' first bit of offense after Marco Estrada had retired the first 10 batters.

Bruce made it 2-0 on his 19th homer, a 442-foot blast to right-center, and Rolen added his fourth homer later in the inning for a 3-0 lead.

Estrada (0-4) allowed all three homers and gave up seven hits in all over seven innings. He is winless since Aug. 23, 2011.

GAME NOTEBOOK: Braun reached 1,000 hits in 815 games, tied for the fourth-fastest among active players with Juan Pierre. Only Ichiro Suzuki (696), Derek Jeter (780) and Albert Pujols (806) did it faster. … There has been at least one home run in 73 consecutive games at Great American Ball Park, the longest streak in the majors since an 80-game streak at Coors Field in 2002-03. … Bruce has 21 career home runs against the Brewers, his most against any team. … Milwaukee's Corey Hart went 0-for-4, snapping his hitting streak at 12 games.