But all that seemed to be turning into the Bucs' favor in the seventh inning of Sunday's series finale was halted by a stingy Royals bullpen, as the Pirates fell just short of completing a three-game sweep, dropping this one, 3-2, in front of 25,888 at PNC Park.
Greinke, sporting his Major League-low 1.90 ERA, arrived as good as advertised on Sunday. Those runs of success that the Pirates have had against some of baseball's best pitchers this season -- Johan Santana, Jake Peavy, Roy Oswalt, to name a few -- sure didn't do anything to help ensure a successful afternoon against Greinke.
"We knew it was going to be a tough go for us," said second baseman Freddy Sanchez, who was 0-for-4 on the day. "We battled, but he did a great job. He's one of the best in baseball and he showed why today."
Greinke became the fourth pitcher this season to reach the 10-win plateau with his 6 1/3-inning, rain-shortened performance. The delay, which came just as the Pirates were stirring up some trouble in the seventh, was the only reason Greinke's outing ended that early, as he had thrown just 80 pitches up until that point.
"You can tell why he's been so dominant as of late," shortstop Jack Wilson said. "He has good stuff."
"It felt good," Greinke said. "It felt like I could throw the ball wherever I wanted to."
Through six innings, the Pirates had five singles to show for their efforts. Pittsburgh had its first legitimate chance in the sixth, when with two outs, Nyjer Morgan advanced from first to third on Greinke's biggest mistake up to that point -- a throwing error on his pickoff attempt.
But the right-hander responded to his error with five mid-90s fastballs to Sanchez, eventually getting the second baseman to ground out on a 97-mph heater to end the inning.
"He has that ability to step it up when he needs to," manager John Russell said. "He's pretty special."
"You have to tip your hat to him," Sanchez said.
Adam LaRoche was the only one with any sustained success against Greinke, and the first baseman got things going in the seventh with a leadoff single, his third in as many at-bats. With one out and the Pirates trailing by three, younger brother, Andy, then drove him in with a triple off the right-field wall.
And then came the rain, halting the game for nearly an hour.
The good news would be that Greinke couldn't return. However, Russell contended afterward that not all was positive in the delay.
"We got him out of the game, but I think it might have squashed a little bit of the momentum," Russell said. "We had something exciting going right there, and then the rain came."
The Pirates were able to score once more, with Andy LaRoche coming home on a groundout. But Pittsburgh went 0-for-11 against three Kansas City relievers, who stalled any thoughts of a comeback attempt.
Right-hander Charlie Morton earned the task of opposing Greinke, and while Morton matched Greinke with zeros through the first three frames, he couldn't sustain it.
"I knew going into today that I was going up against a good pitcher, but at the same time, I don't want to make it an issue," Morton said. "It shouldn't be an issue in my head. He's a good pitcher."
Armed with an effective sinking fastball, Morton mowed through Kansas City's lineup with little resistance the first time through. He faced the minimum through three, with the only hit he allowed being erased on a double play.
The trouble for Morton, though, began in the fourth, when he continued falling behind hitters with too much regularity. Morton served up a leadoff solo homer to Royals outfielder David DeJesus, which was one of six hits the right-hander gave up in the fourth and fifth.
"They found some holes on him," Russell said, "but all and all, I thought he threw the ball well."
Kansas City tacked on two more in the fifth with an RBI double by Mark Teahen and then his nifty slide. With one out and the Royals leading, 2-0, first baseman Adam LaRoche tried to throw out Teahen at the plate. But the Royals third baseman slid under the tag attempt by Jason Jaramillo to score the second run of the inning.
Morton's day ended after those five innings. He gave up seven hits in all and struck out three. Of the 21 hitters he faced, he threw a first-pitch strike to just 11, and he threw at least five pitches in 10 of those 21 at-bats.
"It was all right, mediocre," Morton said, assessing his day. "I didn't really execute pitches. I wish it would have went better. Even if I got ahead, I'd fall into deeper counts, and that was a problem. [I was] not really maintaining the momentum that I had going. I just didn't pitch as well as I had hoped."
On an encouraging note, Morton said he felt no discomfort in his left hamstring, which has kept him from making regular starts since being called up from Triple-A on June 10. He's skipped one start completely, been pushed back another time and now logged 11 innings in three starts.
Even with a limited sample size, there are those who like what they've seen so far.
"I'm looking forward to him making his next start and continuing on," Russell said. "I think he's going to do a very good job for us. I thought he threw well."
The loss kept the Pirates from securing their first sweep of an American League team since 2001, but the club did end Interleague Play with an 8-7 record, its first above-.500 mark in eight seasons.
Jenifer Langosch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.