KANSAS CITY -- Astros right-hander Zack Greinke reached a couple of personal milestones on Saturday night against his former club, the Royals. Asked by reporters how he felt about finally getting a win at Kauffman Stadium as a visitor, while also becoming the second active pitcher to earn wins against every Major League team, Greinke responded like he often does: with few words.

Relying on his slow curve, which sometimes dipped below 70 mph, Greinke limited the Royals to a run, six hits and no walks with seven strikeouts over six innings in the Astros’ 6-1 series-clinching victory at The K, where he pitched home games from 2004-2010.

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“I had planned on using the curve, and it was pretty good at the start, so I used it a little more than I planned on,” said Greinke, who won the American League Cy Young Award with the Royals in 2009. “It’s one of my better pitches, so I thought it would be a good option. I just threw what was called for the most part. I thought everything was good today, except for a couple of mistakes.”

Houston also lowered its magic number to 6 to clinch the AL West title, with the second-place A’s staying 7 1/2 games back with an 8-6 win over the Rangers.

Astros rookie outfielder Kyle Tucker logged a career-high four hits, all singles, including the go-ahead RBI in the sixth. His chance for a 5-for-5 night was denied by drawing an intentional walk to load the bases in the ninth.

Alex Bregman hit his career-high 36th home run, and Yordan Alvarez added a pinch-hit, three-run homer in the eighth to break open a one-run game.

Greinke improved to 16-5 overall and 6-1 in eight starts since joining Houston. It was his first win in five career road starts against the Royals. Greinke joined Nationals ace Max Scherzer as the only active pitchers who have recorded victories against every MLB club.

Greinke said the only player left in Kansas City from his time with the Royals is outfielder Alex Gordon. But there are coaches, including manager Ned Yost. And Greinke has always liked the aesthetics of Kauffman Stadium, notably the sound the fountains make. He’s just not that nostalgic about it.

“I guess it’s nice,” Greinke said of beating the Royals in his former home ballpark. “I pitched a couple of good games here, a couple of bad games. I do like this stadium. It’s got a good feel.”

On beating every MLB team, he said: “Nah, I haven’t thought too much about it. I don’t really have an answer.”

Fair enough. The Astros are fine with Greinke doing most of his talking on the mound.

“He’s in an elite class of pitcher,” manager AJ Hinch said. “It’s hard to throw a curveball effectively 25 mph slower than your other pitches."

Greinke pitched out of a few jams, stranding runners in scoring position on three occasions. The Royals’ best chance for a big inning might have come in the third inning, when they struck first.

Whit Merrifield knocked in Nicky Lopez with an RBI double in the third inning after a review overturned the initial out call by home-plate umpire Chris Guccione. Replay officials deemed that Lopez’s hand touched the plate before Astros catcher Robinson Chirinos tagged him, and that Chirinos violated the collision rule as he straddled home plate before receiving the relay throw.

Hinch said Guccione did not mention Chirinos violating any rules.

No matter, because Greinke kept the Royals from adding on.

With Merrifield at third base with none out, Adalberto Mondesi hit a weak grounder to second, Jorge Soler struck out on a 69-mph curveball and Hunter Dozier made the final out on a fly ball to center.

He’s amazing out there,” Bregman said. “He can throw the ball wherever he wants it and we have complete confidence in him. That curveball is tough when you’re geared up for 90.”

Hinch also appreciated the contributions made by young hitters such as Tucker and Alvarez. Hinch called Tucker, ranked as the club’s top prospect by MLB Pipeline, a “dangerous hitter,” who is making many of the adjustments he didn’t in previous stints in the Majors.

“Watching him behind the scenes, I think he’s much more prepared for the opportunity this time,” Hinch said. “We told him that he’d get more opportunities if he produced more.”

Tucker, while being a left-handed batter, is showing the ability to hit left-handed pitchers like he did in the Minors.

“It feels a little simpler for me against lefties up there,” said Tucker, who slashed .271/.348/.557 in 140 at-bats against lefties in the Minors -- like his results against righties.

“I feel comfortable up there against lefties. For the most part, I see fastball-slider from lefties. They won’t try changeups. Against righties, it could be fastball-cutter-slider-change. You might have to think a little bit more about what they might throw.”