Corey Koskie homered for the Brewers and Bush (5-6) earned his second victory since May 12. He scattered nine hits, struck out eight and walked none in 7 1/3 innings.
"I gave up a lot of hits, but I was keeping the ball down so most of the hits were on the ground -- groundball singles," Bush said. "I was able to get out of a couple of jams, make pitches when I needed to."
Jenkins, who popped out as a pinch-hitter Wednesday to snap his six-game hitting streak, had a two-run double in the first and a run-scoring single in the third.
"Jenks had a big night," Brewers manager Ned Yost said. "His numbers against right-handers are over .300. He's been one of our hottest hitters."
"Anytime you get three runs even before you go out there is a big help, and they tacked on a couple of more a couple of innings later," Bush said. "That lets me relax."
Bush's eight strikeouts were one shy of his season high.
"Most of them I was able to expand the zone," Bush said. "I was ahead in the count and I was able to work the pitches the way I wanted to. When you throw your fastball for strikes, your curveball is more effective. I don't have anything particularly overpowering. I know that and I think everybody else knows that. I try to throw strikes and keep the ball moving. I had good movement and a good sinker."
Hall, who had two hits and a walk, scored three runs for the Brewers, who have won five of seven to even their record at 37-37. The Royals had their season-best four-game winning streak snapped.
"We get to that .500 mark and have been stepping on our feet a little bit and going back a couple of games," Jenkins said. "Hopefully, we can get over that hump."
The Brewers were last over .500 on May 29, when they were 26-25.
Royals rookie Bobby Keppel lasted just 2 1/3 innings in his fifth big-league start, giving up five runs. Keppel (0-4) faced 17 batters and 10 reached base. He allowed eight hits, one walk and hit a batter with a pitch.
"The last hitter I faced was kind of indicative of how the game went for me," Keppel said. "It was a changeup and he hit a three-hopper that found the hole. If it is two feet to the left, it's a double play. That's how the game went. The home run was not a bad pitch. It was down. I'll take that first pitch to him all day."
In his first two starts, Keppel gave up three runs in 14 2/3 innings. In his past three starts, he has allowed 12 runs in 10 2/3 innings.
"Nothing is different," Keppel said. "I would say the percentages of the game kind of went against me today. I threw 64 pitches and 42 were for strikes. I was attacking the zone. Some balls were hit hard and other balls found holes. The first couple of games, they were at people. Today they found holes."
Royals catcher John Buck singled in his first three at-bats and walked in the ninth inning to reach base safely 10 straight times -- five hits, three walks and two hit by pitches -- which is one shy of the club record. Three players hold the mark, last accomplished by Joe Randa in 1999.
"I'll never complain about being on base," Buck said. "Hopefully, I can continue it."
The Brewers improved to 64-70 in interleague play, including 6-4 this season. ... Right-hander Denny Bautista, who began the season in Kansas City's rotation, is struggling with Triple-A Omaha, where he is 0-2 with a 9.00 ERA in three starts since his demotion. He gave up seven runs in three innings Thursday in a loss at Iowa.