CINCINNATI — Zack Greinke was due, and Reds manager Dusty Baker knew it.

“You’re always a little apprehensive and nervous when a guy of that quality is 1-8,” Baker said. “You figure the law of averages is on his side.”

Greinke struck out 12 in a five-hitter, ending a personal four-start skid and leading the Kansas City Royals to a 7-3 victory over Cincinnati on Sunday.

Greinke (2-8) allowed two solo homers to Joey Votto but was in control throughout his first victory since May 13 against Cleveland and his second complete game of the season.

The reigning AL Cy Young Award winner benefited from some rare run support. Kansas City hadn’t scored more than six runs in any game while Greinke was on mound.

“One or two runs don’t matter, but getting four runs at the end of the game made it a lot easier to pitch,” he said.

Billy Butler set season highs with four hits, including a homer, and four RBIs for Kansas City, which took two of three in the weekend series. David DeJesus went 3 for 3 with a homer and scored four times.

“We’ve had a stretch of games where we haven’t scored a lot of runs,” Butler said. “I hadn’t been able to get the pitchers to come to me. They were pitching me tough — pounding me inside. Today, I was able to get them to come to me. I was able to stay back on the off-speed pitches.”

The Royals scored six runs with two out, including Butler’s two-run shot in the fifth that gave them a 3-2 lead. DeJesus singled and stole second before Butler hit a 1-0 pitch from Sam LeCure over the wall in center for his sixth homer and first since May 26 against Texas.

Butler added a two-run double in the seventh after the Royals chased LeCure (1-3), making it 5-2.

“That double to right field was huge,” Kansas City managed Ned Yost said. “As long as he’s driving in runs, I don’t care how he does it.”

Butler also doubled in the ninth to make it seven hits in his last eight at-bats.

LeCure allowed four runs and six hits in 6 2-3 innings. The rookie right-hander has faced Cy Young winners Greinke and St. Louis’ Chris Carpenter and tough San Francisco starter Matt Cain in his last three games.

“I plan to play this game a long time, and if I want to be considered legitimate, then I have to prove that I can beat those guys,” LeCure said.

DeJesus connected in the ninth against Nick Masset, hitting the struggling reliever’s first pitch to him deep to center.

Votto hit his 13th homer in the bottom half but Greinke responded by striking out Jonny Gomes and Jay Bruce to end the game.

“You can see why he won the Cy Young Award,” Baker said.

Votto also went deep in the first and Miguel Cairo had an RBI groundout as Cincinnati took a 2-1 lead.

NOTES: Royals C Jason Kendall went 0 for 5 and is mired in a 1-for-28 skid. … Reds 2B Brandon Phillips was scratched with a cramp in his right hamstring, which also forced him out of a game against Pittsburgh on May 27. Phillips had started every game this season and missed just five innings. His 15-game hitting streak is Cincinnati’s longest of the season and the longest current streak in the majors.