Detroit's Curtis Granderson hits a two-run home run in the Tigers' 13-4 rout of the Royals. Detroit won on Sunday in Kansas City, Mo.

Detroit's Sean Casey, right, greets Craig Monroe after Monroe's two-run home run in the second inning. The homer helped the Tigers rough up the Royals, 13-4, on Sunday in Kansas City, Mo.

Kansas City, Mo. ? Maybe it’s Kansas City’s juicy barbecue ribs that bring out the best in the Detroit Tigers. Or maybe it’s the fact the Tigers are very good these days and the perpetually rebuilding Royals are losing 100 games a year.

For whatever reason, the Tigers are almost unbeatable when they set foot in Kauffman Stadium.

Craig Monroe, Curtis Granderson and Gary Sheffield hit two-run homers in the second inning Sunday, and Detroit beat the Royals, 13-4, for its seventh straight victory overall and 14th win in its last 15 games in the Royals’ home park.

“All the games we win are not in this park,” said Ivan Rodriguez, who had two singles as the Tigers finished with a season-high 17 hits. “We’ve been winning in other parks, too. We play the game hard every day.”

Monroe and Neifi Perez, who also homered, had four RBIs, and Granderson drove in three runs. The Tigers, who haven’t lost since April 28, outscored the Royals 26-12 in sweeping the three-game series.

“We swung the bats obviously very well,” manager Jim Leyland said. “We’re swinging pretty good.”

The defending AL champions had six doubles, a triple and four homers in their latest win.

“We come out and prepare to win every day,” Monroe said. “We know how to prepare. The attitude on this team is we’re going to accomplish the things we’re trying to accomplish.”

Chad Durbin (2-1) gave up two runs and six hits in 7 2/3 innings, with three strikeouts and no walks. He cruised into the eighth with a two-hit shutout but the Royals loaded the bases with three singles and scored a run on Shane Costa’s double-play grounder. Tony Pena Jr. then chased Durbin with an RBI double.

Right-hander Aquilino Lopez, who was called up Saturday night after Joel Zumaya went on the disabled list with a strained right middle finger, came in and got Billy Butler to fly out to end the inning.

Zack Greinke (1-4) allowed six runs and nine hits in four innings. In his previous outing against the Tigers on April 16, he failed to get out of the first inning, allowing three hits and four runs on Rodriguez’s grand slam.

“Greinke, the last two times we caught him, we caught him on days he wasn’t very good. But he’s got outstanding stuff,” Leyland said.

Greinke kept getting behind hitters all day and said he was not surprised to see the home runs start flying over the fence.

“No, because I pitched bad enough and they were hitting it hard enough,” he said. “I gave them too many pitches up and over the plate. I wasn’t getting them off balance and I wasn’t making them hit pitchers’ pitches. There was no rhythm and I never got into a groove at all.”

The home runs in the second inning by Granderson, Sheffield and Monroe gave Durbin a 6-0 lead to work with.

Then the Tigers added three in the sixth on RBI doubles by Monroe and Perez and Granderson’s RBI single.

Monroe’s run-scoring single ignited a four-run seventh for the Tigers. After Brandon Inge’s double made it 11-0, Perez hit his first home run of the year.

The Tigers said after the game that Zumaya would see a hand specialist in New York on Monday and only then would they know the extent of his injury.

Zumaya heard a “pop” while warming up in the bullpen Saturday night. He had a thick bandage on the finger Sunday and described the sensation as a “shocking pain.”

“It’s hurting now. It hurts, and that’s it,” he said. “And it’s swollen.”

Detroit’s only loss in Kansas City since 2005 was a 3-1 setback on April 6.

Notes: Leyland planned to jump on a plane as soon as the game was over and fly to Pittsburgh for a brief visit on a day off for the team. He maintains a home there. … Rain delayed the start of the game by 26 minutes. … It was Durbin’s 28th start in Kansas City. He played for the Royals from 1999-2000.