MILWAUKEE - It had been a frustrating day for Billy Hamilton.

The Cincinnati Reds' speedy outfielder had gone without a hit in his first four at-bats Friday, and for his fifth at-bat, he had to face Milwaukee Brewers closer Francisco Rodriguez.

But the worm turned for Hamilton, who ripped a 1-0 fastball into right field to score shortstop Zack Cozart in the top of the ninth inning as the Reds beat Milwaukee 6-5 at Miller Park.

"Billy came up big time," Reds manager Bryan Price said. "That's a huge hit, simply because it doesn't put [Todd] Frazier [the next hitter] in that two-out situation where he has to drive him in, takes a little pressure off the next guy, which was great, and certainly set the table for [right-hander Aroldis] Chapman to come in and do his thing."

Chapman did just that, striking out two batters in his perfect ninth inning to record his 11th save of the season.

Cincinnati starter Homer Bailey did not factor into the decision but got off to a good start, holding Milwaukee to a run through six innings before running out of gas in the seventh.

"After we scored all those runs, the thing I wanted to do was go out there and put up some quick zeroes, get us back in the dugout, try to tack on a few more," Bailey said. "But, did that for two and that last inning I just couldn't find a way to get out of it."

Milwaukee starter Matt Garza pitched well, allowing seven hits and a walk over seven innings of work, but hurt himself with two crucial errors, resulting in four unearned runs.

"It hurt him and it's too bad because he really had good stuff today," Brewers manager Ron Roenicke said.

The Reds took a 1-0 lead on Garza in the first, when Garza botched a throw to second on Frazier's stolen base attempt. Frazier went to third on the play and scored on second baseman Brandon Phillips' single.

Milwaukee got the run back in the fourth on an RBI double by third baseman Aramis Ramirez, but in the fifth, Cincinnati created some breathing room thanks to another Garza miscue.

Cozart singled to open the inning, bringing up Bailey, who laid down a sacrifice bunt that Garza charged and scooped up.

But Garza's throw sailed well over first baseman Mark Reynolds' head and into the stands down the first-base line, putting runners at second and third with nobody out.

"Everything felt great," Garza said. "It's a shame I let it go to waste on throwing errors. It just sucks. The guys battled back. We lost it late, but we should have never been in that spot. My stuff was too good tonight to do something dumb like that. I had two good outings where I made all my plays and battled. Tonight I had all my stuff and made two bad plays."

A perfect throw from center fielder Carlos Gomez kept Cozart at third on Hamilton's fly to center, but back-to-back singles by Frazier and first baseman Joey Votto, followed by a sacrifice fly by Phillips put the Reds up 4-1.

Cincinnati added another run when Brewers left fielder Khris Davis was charged with an error on right fielder Jay Bruce's double before Garza finally got out of the inning.

Davis sparked Milwaukee's comeback in the seventh, leading off the inning with his 11th home run of the season. The Brewers finally tied the game on Gomez's two-out double, but they left runners at second and third when Ramirez ended the inning with a grounder to short.

"A sloppy game is always discouraging and it was sloppy but it wasn't just Garza," said Roenicke, whose team committed four errors. "That's always disappointing, but I'm glad guys were able to battle back. It was good to come back and at least make it a ball game. I felt really good when we came back and tied it; I thought we were going to win."

The Reds have won three in a row against Milwaukee this season and are 4-1 against the Brewers overall.

NOTES: Milwaukee optioned INF Irving Falu and OF Logan Schafer to Triple-A Nashville after the game. The Brewers plan to recall UTL Elian Herrera from Nashville and activate LHP Tom Gorzelanny from the disabled list Saturday. ... Cincinnati RHP Mat Latos will make his 2014 debut Saturday against the Brewers at Miller Park. Latos underwent knee surgery during spring training and then had his comeback delayed by a strained elbow. When he was finally available for a minor league rehab assignment, Latos posted a 2.33 ERA in four starts and threw as many as 81 pitches. ... The Brewers recognized more than 50 former players Friday while dedicating a new Wall of Honor at Miller Park. ... The Reds took three of four from Milwaukee earlier this season at Great American Ball Park.