There are just 20 games to go for the Royals, who shrugged off a 16-2 beating on Friday night to win for the 10th time in their last 14 games.
"Every win is good," Perez said. "The last 20 games are going to be good for us. We're going to play hard every night, every day and we'll see what happens."
What happened later on Saturday night was that Tampa Bay lost at Seattle, enabling the Royals to move to with 3 1/2 games of the second Wild Card spot.
Justin Verlander, Detroit's five-time All-Star, came into his 28th career start against Kansas City with a 15-4 record. But, because of Perez's home run, Verlander is 0-3 this year and the Royals have won all five games that he started against them.
"You can say what you want -- Verlander is tough as nails," Royals manager Ned Yost said. "He's as good as they come and we've done very well against him. They've all been nip-and-tuck, tight one-run games for the most part and we've come out on top, and that's all that matters."
Perez crushed a 1-0 fastball from Verlander, driving it high over the left-field wall for a two-run homer, in the sixth inning to give the Royals a 4-2 lead and 20,402 fans reason to roar. It came with two outs and Eric Hosmer, who had doubled, on base.
"As soon as I hit it, I knew the ball was gone. I hit it pretty good," Perez said.
"It was 98 [mph], it was down and it was in," Verlander said. "It was a good pitch, but he was able to get the barrel on it."
The Tigers cut that lead to 4-3 in the seventh. Two singles off left-handed reliever Will Smith brought right-hander Luke Hochevar out of the bullpen with the right-handed power coming up. Torii Hunter fanned for the second out, but Miguel Cabrera singled to center for the run.
But that's the way it ended with Greg Holland, doing his own bounceback from a blown save on Thursday, pitching a perfect ninth inning with two strikeouts. It gave him 39 saves.
Holland said the Royals learned how to cope with defeat and failure the hard way last year and even during a dismal month of May this season.
"You play too many games to let one game lead into the next because that is how you slump," Holland said. "We learned from that last year getting frustrated and letting the frustration build on itself. You dig yourself an even deeper hole. We've come in here this year, even in May when we really struggled, and we've been upbeat and ready to play that day, and I think that's why we're vastly improved from last year as far as the record goes."
The record now is 74-68, six games over .500.
Royals left-hander Danny Duffy had one of his high pitch-count starts, running up 31 in the first inning but escaping with minimal damage, one run. Duffy opened with a four-pitch walk to Austin Jackson, who got around on a wild pitch and Prince Fielder's single.
After that Duffy got through three scoreless innings but, in the fifth, the Tigers loaded the bases with Nick Castellanos' first big league hit and two walks. There was just one out and the Royals replaced Duffy with right-hander Wade Davis, who was marking his 28th birthday. His gift, as it turned out, was his seventh victory.
Davis struck out Hunter but walked Cabrera on a 3-2 pitch to force in a run.
"I've faced him a lot and I know what he was trying to do. I wasn't going to give in and give him something to whack off the wall or over it so it was a [yucky] walk, but it paid off," Davis said.
Davis ended the inning by getting Fielder to pop out.
David Lough led off the Royals' third inning with a double to left center and was bunted to third. But, for the second night in a row, first baseman Fielder grabbed a grounder, this one by Alcides Escobar, and threw out a runner at the plate. Lough slid hard into catcher Brayan Pena and limped away, but remained in the game.
Escobar got to third on Alex Gordon's single and raced home on a squeeze as Emilio Bonifacio dropped a flawless bunt single toward creaky third baseman Cabrera with two out.
Bonifacio and Escobar cooked up the play themselves.
"I just tell him and he knows that every time he's there that there's a pretty good chance that I'll bunt for a base hit," Bonifacio said. "With a tough guy like Verlander, I want to make sure I don't mess it up."
It couldn't have gone better.
"It was an absolutely perfect bunt to score Esky and get us back into a tie," Yost said. "That's what Bonny does. He's got a bunch of tools in his repertoire that he can use to help you win ballgames."
The Royals gained a 2-2 tie in the fifth as Jarrod Dyson walked, stole his 30th base and raced home on Escobar's lined single to left.
The stretch run is on and even the usually stolid Yost admitted that, at this point, each victory can be exhilarating.
"I'd be a liar if I said no. Yes, very exhilarating," Yost said. "Every win means something, every pitch means something. ... Every game is really crucial and every game is important."