DETROIT -- Will Rhymes' day began with a lunch order from Chipotle that he could stare at but couldn't eat, because he forgot his wallet. After further review, it ended with a bottle of Dom Perignon waiting in his locker at Comerica Park.

That's what a go-ahead run on a first Major League homer off Zack Greinke will do.

"I think that's been sitting on ice for a while," Rhymes joked about his gift from Brandon Inge after powering the Tigers to a 7-5 win over the Royals on Monday night. "A couple hundred at-bats, at least."

OK, Rhymes hadn't gone that long in the big leagues without a home run. But he could have without much surprise. As it was, after 164 at-bats, it was worth the wait.

His listed height of 5-foot-9 might be a bit generous, but his first Major League home run was not. Cy Young Award-winners don't give up a lot of cheapies, and Greinke hadn't given up a home run to any Tiger in 66 innings. AL MVP candidate Miguel Cabrera has never homered off of him.

Normally when Greinke gets a Royals rally and a middle-inning lead, it's time for him to shut down the opposition. With eight straight Tigers retired heading into the sixth inning and a 5-4 lead in his favor, thanks to a five-run Royals fifth, he was well on his way.

After an Alex Avila leadoff single, Greinke regrouped to strike out Inge and retire Ramon Santiago, leaving Rhymes trying to continue the rally. He saw some of the best of Greinke last month in Kansas City, from a nasty changeup to a slider that he called "unhittable," so he sat on a fastball.

He had a first-pitch fastball away that he passed up for strike one because he knew he couldn't drive it to the right side where he wanted. Once he got a fastball in and lofted it right, all Greinke could do was shrug.

"I thought it was a pop up leaving the bat," Greinke said. "It just kept going. He knew he hit it good, looking back on it. He thought it had a chance. Obviously, he hit it really well. But off the bat, I thought it was going to be just a routine popup."

That's excusable. The umpires initially thought it was a game-tying triple off the fence. So did Rhymes.

"I was running and just hoping he didn't catch it," Rhymes said. "I didn't get a look at it at all. I was just hoping to see the ball come back down to land somewhere."

Umpires initially ruled the ball hit off the top of the fence and stayed in play, which would have made it a game-tying triple. Replays, however, showed the ball hit off the lower half of the railing above the fence. Once umpires came to the same conclusion and overturned their original call, Rhymes trotted home with the go-ahead run and gave Johnny Damon a leaping high-five.

"I got to enjoy that home run a lot longer than most people do," Rhymes said. "That was the longest home-run jog ever."

He also gave the Tigers bullpen a lead it protected the rest of the way with some defensive help from a couple other rookies. Back-to-back hits from Wilson Betemit and Kila Ka'aihue seemingly had the Royals rallying again in the seventh, putting runners at the corners with one out. But Ka'aihue tried to stretch his line drive into a double on Casper Wells, who entered the game just a few batters earlier as a defensive replacement.

Wells fired a strike to second to nab Ka'aihue and take a sacrifice fly chance out of play.

"You have to make him make the play," Royals manager Ned Yost said. "The ball made a perfect bounce right back to him and he made a perfect throw."

Three pitches later, Avila made close to a perfect flip over the railing of the Royals dugout to catch Brayan Pena's popup to end the inning. It was a solid enough play that even Yost had to compliment him as he kept him from falling headfirst.

"That's a long ways down," Avila said. "As soon as I went over, I was looking straight down and all you see is that wood and concrete there. You feel like you're 100 feet off the ground."

Avila added an insurance run in the eighth when he took a Jesse Chavez pitch deep for his sixth home run of the year, a no-doubt drive to left. But no tape-measure shot was topping Rhymes, whose power is anything but routine.

"I hope he doesn't try to live [hitting the ball] in the air," manager Jim Leyland said.

He won't, but his power isn't rare; he homered twice for Triple-A Toledo this season, and had 18 over six Minor League seasons. But most of his power goes into line drives into the gap for doubles, not putting the ball in the air.

"Obviously, it's not something I'm going out there trying to do," he said. "It's just one of those things that happens every once in a while. But there's not a much better feeling for anyone, even guys who do it all the time, than to hit a home run. So it feels good. I'm not going to be up there trying to repeat it every night. That's gotten me in trouble in the past. But yeah, I'm certainly going to enjoy this.

"I'm glad it could come in a win. That really makes it so much better."