"I'm going to go out and light some fireworks -- with my right hand," said Davis, a left-hander.
Davis (5-5) gave up two runs and six hits in 8 2/3 innings, and the Brewers shook off their slow start against Bronson Arroyo to score five runs in the fourth inning and send the Reds to their fourth straight loss.
"You face a pitcher like Bronson Arroyo, you know you've got to keep that opposing team down as much as you can, because you're not going to get many chances to score runs," manager Ned Yost said. "Doug did that today."
Arroyo was even better than Davis through the first three innings, sitting down the first nine batters he faced before running into trouble in the fourth.
"Well, it was just one of those innings where you lose a ballgame," Arroyo said. "You can't just give up five and expect to win, especially when the other guy is throwing that well. And Doug Davis pitched a heck of a game."
Arroyo walked Rickie Weeks to lead off the inning, and Weeks advanced to second on Bill Hall's bunt single -- the Brewers' first hit of the game.
"He didn't hit a perfect bunt, but good enough," Arroyo said. "And he's got enough speed to beat that out easily and it got me in trouble."
Prince Fielder added a sacrifice fly and Koskie capped off the big inning with his 12th homer.
Koskie said putting the first two runners on base got Arroyo "a little out of sorts."
"You've got to look at that whole inning," Koskie said. "It started off with Billy's bunt, and that was big for us."
Arroyo (9-5), who started the season 5-0, gave up five hits and five runs in seven innings. He struck out six and walked three. Arroyo was 2-1 with a 2.45 ERA in three previous starts against the Brewers this season.
"Sometimes an inning like that can explode on you, and it did," Arroyo said.
Davis never gave up that big inning -- a possible sign that missing his most recent start against the Chicago Cubs on Thursday with a stiff back might have helped him.
"It very well could have, and that was the idea behind it," Yost said.
Davis struck out six and walked three. Yost allowed him to take the mound in the ninth, and he got two outs before allowing a single to Rich Aurilia and a walk to Austin Kearns.
Yost pulled him in favor of Brian Shouse, who got pinch-hitter Ryan Freel to fly out for second save in three chances.
"I wanted to finish the game, and I had a chance to," Davis said.
Kearns doubled with two outs in the seventh, the first hit Davis had given up since Scott Hatteberg's single in the second. Hatteberg then hit his seventh homer of the season on a 1-0 pitch to cut the Brewers' lead to 5-2.
It was the Reds' first scoring chance since the first inning, when Brandon Phillips led off the game with a single for the Reds but was picked off. Adam Dunn singled, but was doubled up by Jenkins after a flyball to right field by Ken Griffey Jr.
"We really didn't get anything going all day besides that, other than the home run by Hatty," Reds manager Jerry Narron said.
- Brewers ace Ben Sheets, who has missed most of the season with tendinitis in his right shoulder, threw a three-inning, 45-pitch simulated game Tuesday. Brewers manager Ned Yost said Sheets threw great, but team officials would wait to see how he feels Wednesday before deciding whether to send him to the minor leagues for a rehabilitation stint.
- Milwaukee catcher Damian Miller was scratched from the lineup because of dizziness and replaced by Chad Moeller.
- Tuesday's attendance was 39,280.