KANSAS CITY -- The Tigers flirted with danger all night, but the hottest team in baseball escaped jam after jam before Parker Meadows played hero with a broken-bat single in the 10th to charge a 3-1 extra-inning victory over the Royals at Kauffman Stadium.

Detroit has now won 24 of its past 34 games -- the most in the Majors in that span -- and stayed 1 1/2 games behind Minnesota, which holds the head-to-head tiebreaker, for the third and final AL Wild Card spot.

But it wasn’t easy -- at all.

The Royals flooded the basepaths while the Tigers had trouble solving Kansas City starter Cole Ragans for seven innings, but Detroit’s young core once again stepped up to take its postseason push another step forward.

On Tuesday, it was Meadows who made the latest imprint on the Tigers’ improbable postseason run. The 24-year-old center fielder saved at least one, if not two runs, with a spectacular sprinting catch in the third inning. Hunter Renfroe smacked a 103.7 mph line drive to straightaway center, but Meadows raced 27.6 feet/second to cover 80 feet in 4.8 seconds to rob the Royals of the lead.

“I always think Parker can get it. … But it was hit hard, and it was hit to the big part of the ballpark, and it was just a matter of if he took the right angle. He’s generally going to run down 99.9999% of them that stay in the yard,” manager A.J. Hinch said. “But man, and we held our breath a little bit because of how much damage it could have done to the inning. We were all super pumped whenever he came down with it.”

Meadows’ run-saving play was the theme for the Tigers on Tuesday, who just continue to find ways to win games. Casey Mize didn’t have his best stuff, only getting through 4 1/3 frames and allowing at least one baserunner in all five innings, but he rolled two double plays and got help from reliever Shelby Miller to get out of a bases-loaded situation in the fifth.

“We found a way, and so I think that’s obviously the most important thing of what we’re trying to do right now, is we won the game,” Mize said. “It wasn’t pretty or perfect from my end, but I gave it everything I had every pitch and felt like I kept us in it the best I could. Then Shelby comes in and bails me out of it in a huge spot. Our team is resilient and came out on top, so I think that’s what’s most important.”

That resiliency showed up from start to finish as the Tigers, who had a 0.2% chance to make the playoffs on Aug. 10, now play in some of the most important games since the club last made the postseason in 2014.

Miller displayed that when he came back out in the sixth, finding himself in another bases-loaded jam before responding by getting Tommy Pham to fly out to end the threat.

Beau Brieske, Tyler Holton and Jason Foley then combined for four scoreless frames to lower Detroit’s reliever ERA this season to 3.57 -- the 5th best in the Majors -- despite throwing the most innings in the big leagues.

“I think we were amazed at first [with the bullpen], and now it’s just like, yeah, that’s what they do, you know?” Mize said. “We feel good about turning the ball over to them because they’re relentless in the fact that they’re getting outs in a lot of different ways and getting the job done. … That’s where I’m at now. I’m not surprised anymore.”

Foley, who picked up his 25th save of the season, added: “Everyone’s done a hell of a job lately, especially with how much we’ve been having to throw. They’ve just relied on us a lot, but we’ve done a great job.”

Working out of those jams allowed Matt Vierling’s RBI double in the first inning to be enough to get it to extra innings before Meadows and Riley Greene added on in the 10th frame.

And as the Tigers continue to keep their postseason hopes alive, no one inside Detroit’s clubhouse is shocked to watch Meadows play a large role in it.

“At first, [I was] surprised, and then [thought], why am I surprised that Parker’s running down that ball?” Mize said. “But man, we were talking about it up here, like that guy could be a superstar. He’s got it all. And when he runs down a ball like that, just kind of reminds you why. He’s a freak out there. It was amazing.”