By winning to the satisfaction of most of the 17,643 fans, the Royals got back to three games under the .500 mark and 5 1/2 games back of the first-place Tigers.
Kansas City is also in a virtual tie for second place with Cleveland. The Indians stand 30-33 (.476) and the Royals are 29-32 (.475).
"Eventually, if we're going to have a chance to make the postseason, we're going to have to beat teams in our division, so these are all important games for us," said winning pitcher Jeremy Guthrie.
Except for one pitch to Miguel Cabrera -- he pounded a two-run homer -- Guthrie's night went virtually without a hitch. He made it through 6 1/3 innings to improve his record to 7-3 and the bullpen did the rest.
Aaron Crow, Tim Collins, Kelvin Herrera and Greg Holland combined for 2 2/3 scoreless innings. That gave the bullpen 20 2/3 consecutive innings without being charged with a run.
The idea against the Tigers' powerful lineup is to keep the ball inside the park.
"We had 18 fly-ball outs today and the good thing is that they were outs," Royals manager Ned Yost said.
The lone exception was Cabrera's soaring drive over the left-field wall in the third inning.
Cabrera wreaks havoc on a lot of teams and Kansas City is just one of them. He came into this series with a .335 average against the Royals. Sure enough, after Torii Hunter doubled to left field, Cabrera crushed Guthrie's 1-0 pitch.
That increased Cabrera's league-leading RBIs total to 69. It also was his 18th home run this season and the 18th of his career against the Royals.
"We probably hit too many balls in the air, to be honest with you," Tigers manager Jim Leyland said. "But we hit some balls good, we pitched good, we played pretty good. We got beat."
The Tigers' last serious threat came in the seventh when, with one out, Guthrie gave up a single to Avisail Garcia and plunked Andy Dirks with a pitch. Crow arrived from the bullpen with the unenviable task of facing Hunter, already 2-for-3, and Cabrera.
"Their two-through-six lineup is as tough as they come in baseball, so Aaron Crow against Hunter and Cabrera with runners at first and second in a one-run game and to be able to get out of that inning unscathed is huge," Yost said.
Hunter flied out to right field.
"I just tried to get ahead of him," Crow said. "I try to keep the ball low and hopefully he hits a ground-ball double play and I get out of it without having to face Cabrera. I watched the video, that pitch was kind of up and he popped it up."
Then Cabrera struck out on a slider.
"He's by far the best hitter in the game, so you just try to limit the damage he can do," Crow said. "Jeremy gave up the home run, but he limited him in his other at-bats and I was fortunate enough to get him, too."
Tigers right-hander Doug Fister is remembered by the Royals for striking out nine of them in succession last Sept. 27 at Detroit to set an AL record. Salvador Perez, the first of those victims, got a measure of revenge in the bottom of the third as the Royals scored all three of their runs.
Alcides Escobar, breaking an 0-for-12 skid, legged out a ground ball to shortstop Jhonny Peralta to start the inning with a single.
"I need some hits and when I start an inning like that, it's nice," Escobar said.
Alex Gordon popped out, but Eric Hosmer pulled a single into right field. Perez launched a liner and center fielder Garcia raced in and, crossing paths with Hunter the right fielder, missed a diving attempt.
"As an ex-center fielder, [I know] if you see me coming, get out of the way," Hunter said. "So, I saw him running full speed. He didn't say anything, and he took off diving. I said, 'Oh,' and jumped out of the way. That's his ball, and he wants that. He has a right to do it, and I have to get out of the way. I think he dove and wasn't really close."
The ball zipped past the outfielders and Perez was on the way to third.
"He probably shouldn't have dove. Usually, when a righty hits the ball to right-center and stays inside the ball, it fades back to the right fielder. But he's 21. He'll figure it out," Hunter said. "That's why I went after it so aggressively, because it's coming back to me. But I saw him coming. Can you imagine running into 6-5, 250? I'm gonna die. Let him have it."
Perez's two-run triple tied the game, but he stayed at third when Billy Butler grounded out. That left it up to Lorenzo Cain and he flew down to first base, beating Peralta's throw for an RBI single.
"We won the game on an infield hit," Yost said.
Fister pitched the rest of the way for the Tigers and didn't face more than three batters in each of his last five innings. But the Royals had beaten him and the AL Central frontrunners.
Leyland, as is his habit, graciously saluted the Royals.
"Everybody knows they're a really good club," Leyland said. "They had a terrific spring and they got off to a little slow start, but it looks like they're getting into the swing of things now. It's a good club. They've got speed. They've got some power. They upgraded their pitching over the wintertime. Yes, it's a very good club with a good closer."