The victory enabled the Royals to reclaim first place in the American League Central, one-half game ahead of Chicago.
This was the second straight complete game for the Royals. Brian Bannister beat the Minnesota Twins, also 5-1, on Sunday at Kansas City. The Royals' team ERA of 2.46 is the best in the Major Leagues, ahead of the 3.29 by the St. Louis Cardinals.
"Bannister's was great," Greinke said. "He did a lot of that on his own. A couple of mistakes and he had to get a couple extra outs and he made good pitches getting them out. So I was really impressed by that outing.
"But today every ball put in play was at someone or the play was made."
Grudzielanek's 10 assists were just one shy of the Royals' club record of 11 by Cookie Rojas on May 17, 1973, at Texas. Teahen's big play came after Kenji Johjima got the fifth single off Greinke with two outs in the eighth.
Yuniesky Betancourt belted a long drive that appeared to be headed for home-run territory. But Teahen retreated, jumped and hauled it in.
"You breathe a little easier when Teahen makes a great catch like that," manager Trey Hillman said. "It could've tightened some things up a little bit."
"Just the other day [Teahen] was telling me he likes going in more than back," Greinke said. "But not only did he make a play that was textbook, but it was perfectly done. He made it look easy and it definitely wasn't easy going back on a ball in a pressure situation."
Butler cannot be stopped. Not this year so far, anyway. He's hit safely in each of the Royals' 13 games and, for the first time, he banged a home run.
He opened the second inning against left-hander Jarrod Washburn with a blast over the left-field wall. Jose Guillen followed with a double to right-center, snapping a 0-for-12 skid. One out later, Olivo smashed his first home run to left for a 3-0 lead.
"It's not going to be our typical way of scoring runs this year, but we'll take 'em when we get 'em," Hillman said.
Butler's start-of-the-season streak matched the second-longest in club history. Darrell Porter (1978) and Danny Tartabull (1989) also hit in 13 straight. George Brett's streak of 19 games to start 1983 is the record.
"I try to get a hit every day, but I'm not going to get a hit every game," Butler said. "I know it's started out good, but it's only 13 in. You're bound to run into some tough pitching or have a bad day. I just haven't had it yet."
Tony Pena Jr. ended a 0-for-26 swoon with a single in the fifth inning. Pena also singled in the seventh, following Olivo's single and John Buck's walk, to load the bases with no outs. The Royals got just one run out of it, though.
Greinke issued just one walk and, sure enough, that resulted in the only run against him. A run, by the way, that actually increased his ERA from 0.60 to 0.75.
After Brad Wilkerson crossed the plate on a force-out in the third, Greinke faced just 20 more batters -- just one over the minimum.
Hillman had relievers throwing in the bullpen during the seventh and eighth innings while the Royals were busy sending batters to the plate, scoring a run in each inning.
"The only reason I had guys up was that he sat for so long," Hillman said. "We don't want to get caught with our pants down, so to speak."
Greinke went out for the ninth and had a 1-2-3 inning. He'd gone nine innings for the first time; his other complete games were eight and five innings, respectively. He'd thrown 107 pitches and gotten 16 outs via ground balls.
How did he do it?
"Locating in and out. Throwing the slider and breaking ball for strikes early, and what else can you say?" catcher Buck said, then thought of something: "And used his offspeed stuff with just perfect location."