CINCINNATI -- After playing to a scoreless tie for nearly 2 1/2 hours, Billy Hamilton changed Sunday afternoon's game in an instant.

Hamilton scored the winning run from third on a passed ball in the bottom of the ninth inning, lifting the Cincinnati Reds to a 1-0 victory over the Milwaukee Brewers to conclude a three-game series at Great American Ball Park.

"Two outs, nobody on, and he grinds out a walk," Cincinnati manager Bryan Price said. "A few minutes later, game's over."

In the bottom of the ninth, Tyler Thornburg (3-3) walked Hamilton with two outs.

Will Smith came on and walked Joey Votto on six pitches. Hamilton's 24th stolen base put him at third and he raced home when Smith's pitch skipped a few feet away from catcher Jonathan Lucroy.

"From an excitement standpoint ... look, I'm not implying that he's Rickey Henderson or Lou Brock, but he affects the game in that way with his speed," Price said.

Brewers manager Craig Counsell had third baseman Will Middlebrooks playing back, almost conceding a steal.

"More bad things can happen trying to throw him out than letting him steal third," Counsell said.

The ball was only about 10 feet away on the grass to the left of home plate when Hamilton broke for home, but he slid safely underneath a high throw from Lucroy.

"He knows he can get further down the line because he has the speed to get back," Price said.

Hamilton left the clubhouse prior to speaking with reporters following Sunday's game.

Tony Cingrani (2-3) pitched a scoreless ninth inning to earn the win for Cincinnati.

Reds starter Dan Straily allowed only three hits in seven innings with a walk and four strikeouts on 99 pitches.

Brewers starter Zach Davies, who was recalled from Triple-A prior to the game, retired the final 11 batters he faced. He allowed only four hits and struck out five over his seven frames. Reds batters grounded back to the pitcher four times on Sunday.

"There was such limited hard contact for both teams in this game," Price said. "It was great to win this game when we did. You don't want to go into extra innings in a scoreless game."

Davies began his second stint this season with Milwaukee. Sunday's start was his second this season against the Reds. He allowed two earned runs in 5 2/3 innings of a 9-5 Brewers' win on May 27.

Cincinnati threatened against Davies in each of the first two innings Sunday, but he was able to pitch out of trouble. Despite having the leadoff batter on base the first four innings, the Reds couldn't break through.

"Davies pitched really, really well," Counsell said. "He was sharp. That was the purpose of the long layoff was to get him sharp. It worked out really well."

Straily, meanwhile, rolled through the first four innings, allowing just two hits and retiring nine straight batters in one stretch.

The closest either team came to scoring through five innings was when Milwaukee's Kirk Nieuwenhuis hit a drive to right, which was caught at the wall by Jay Bruce leading off the fifth.

Straily didn't walk a batter until Jonathan Villar earned a free pass to begin the sixth. He retired the next three batters in succession to keep the game scoreless.

Both Davies and Straily pitched to contact throughout Sunday's game with only eight combined strikeouts and one walk into the seventh of a scoreless game.

"The slider was a good pitch for me today," Straily said. "I was able to throw my fastball whenever and wherever I wanted to. I felt good all day on the mound. Had good command of everything."

In a game where the margin for error was slim to none, not surprising that a player with the play-making ability of Hamilton proved to be the difference.

"Hamilton is one of the few players who could score on a ball like that," Counsell said.

NOTES: Cincinnati 2B Jose Peraza was caught stealing in the second inning after beginning his career 13-for-13 in stolen base attempts. ... The Reds optioned struggling LHP John Lamb to Triple-A Louisville and recalled OF Kyle Waldrop. Lamb allowed nine earned runs in two innings on Saturday. ... Reds 2B Brandon Phillips was out of the lineup for the second straight day with a strained calf muscle. ... Brewers RF Hernan Perez was out of the starting lineup on Sunday after leaving Saturday's game with a left foot contusion. X-rays were negative.