Royals Hall of Fame member Mark Gubicza, who held the record for almost 21 years, struck out 14 against Minnesota on Aug. 27, 1988.
So after this one, the Indians had plenty to digest.
Fastballs on the corners, looping curveballs, diving sliders, changeups -- the Indians remembered them all.
"That's about as good as I've seen any pitcher in my time here at this level," Indians manager Eric Wedge said. "He had special stuff tonight. He always has special stuff."
Greinke allowed two earned runs over his eight innings of work and lowered his American League-leading ERA to 2.43.
And counting reliever Robinson Tejeda's one strikeout in the ninth, the Indians set a season high by striking out 16 times.
Greinke started in a hurry, striking out two in the first and two more in the second. He struck out Matt LaPorta swinging in the third for his fifth strikeout and added two more in the fourth, sitting down Shin-Soo Choo and Jhonny Peralta to start the inning.
Greinke was even better in the fifth, striking out Luis Valbuena, Kelly Shoppach and LaPorta in order to get to 10 K's.
"We tried to talk about it -- tried to say, 'What'd he throw to you?'" Peralta said.
It didn't help.
Greinke fanned two more Indians in the sixth and two more in the seventh, including the record-tying strikeout against Shoppach to end the seventh. Shoppach and Choo led the way by striking out three times each.
And then in the eighth, with the Kauffman Stadium crowd on its feet, Greinke broke the record by striking out Andy Marte -- the same Marte who had earlier broken Greinke's shutout with a solo homer in the sixth.
"He was just throwing anything and everything up there," right fieder Jamey Carroll said. "[And] different speeds, so there was no pattern and you couldn't get any sort of rhythm."
Greinke recorded more than 10 punchouts for the fifth time this season, broke his old career high of 11, and set a season high for strikeouts (197) in the process.
"He had everything working," Wedge said. "And for a young pitcher -- I think we've talked about this before -- he pitches smart. We saw him when he was younger when he was trying to figure it out. And now he's a full-fledged pitcher with stuff, composure, and he did a great job tonight."
And Greinke, who recorded his 21st quality start and improved to 12-8, is now 2-0 against the Indians this year, with 38 strikeouts in four starts.
There was only one question left for Wedge: Is Greinke -- with his league-leading ERA and filthy repertoire -- the best pitcher in the league?
"He's one of them," Wedge said. "I don't want to slight anybody else, but there's probably four or five guys that you could probably make that argument for. But I think you'd be hard-pressed to see somebody throw a better ballgame than what he threw tonight."