Here, finally, on edge of September are the Royals as they hoped to be.

A pulsating 2-1 victory on Thursday completed a three-game sweep of second-place Detroit and followed a three-game sweep over first-place Chicago when the Royals were last here at Kauffman Stadium.

And yes, sadly, it’s too late to mean much this year in the standings, but, just maybe, it allows them (and us) to hold firm to a belief that better times are within reach in the not-too-distant future.

“We can play with these guys,” left fielder Alex Gordon said. “We knew that coming into this year. We just started off slow. I wish we hadn’t done that. All we can do now is battle.”

This latest victory stemmed, foremost, from another marvelous outing by veteran right-hander Jeremy Guthrie, who carried a 2-0 lead into the eighth inning before things got interesting.

Guthrie, 3-3, produced his fifth quality start in his last six outings and bounced back big from a rough go last time out in Boston. This marked the fourth time in five starts that he permitted fewer than two earned runs.

“I was going to go out there and throw strikes,” said Guthrie, who permitted 10 hits but only one run. “When you throw strikes, guys are going to put some swings on it. The biggest thing is I was able to keep nine of them to singles.”

It was a wild ending, though. First, the Tigers scored once in the eighth, when Tim Collins permitted an inherited runner to score, before Aaron Crow stranded the tying and go-ahead runs.

The Royals then turned to Kelvin Herrera to protect a one-run lead in the ninth after closer Greg Holland had labored through high-leverage saves in the series’ two previous games.

“I was a little bit nervous to be honest,” Herrera said. “It was my first save opportunity in the big leagues.”

It showed.

Herrera started the inning with a four-pitch walk to pinch-hitter Alex Avila before Lorenzo Cain made a diving catch on Austin Jackson’s sinking liner to center field. The Royals got a similar web gem Wednesday in the ninth inning from Jarrod Dyson.

“Give it up for my man,” Dyson said. “That’s a great catch.”

The speedy Jackson might have circled the bases if the ball gets past Cain.

There’s more.

Right fielder Jeff Francoeur tried for a diving catch on Andy Dirks’ sinking liner but short-hopped the ball. The result was a single that moved Avila to second.

That got the game to Miguel Cabrera, a perennial MVP candidate who is a long-time Royals’ killer — 16 homers, 60 RBIs and a .333 average in 83 previous games.

Herrera got Cabrera to hit a medium grounder to second that turned into a game-ending double play, an amazing double play. Shortstop Alcides Escobar, after taking the throw from Johnny Giavotella, had to leap a sliding Dirks before throwing to first.

“I saw him land (after the leap),” third baseman Mike Moustakas said, “and I thought, ‘OK, we’ve got to get Prince (Fielder). Then he threw it and … we just won? What in the world just happened?’ ”

Escobar’s throw just beat Cabrera, and the game was over.

“Oh, man,” Escobar said. “I knew if I threw the ball when I jumped, I might make a bad throw. I knew Miguel Cabrera was running, so I wanted to make sure to make a good throw. But that was no easy play in that situation.”

Guthrie had the victory. Herrera had his first major-league save.

And the Royals had a sweep. Look, they’re still 12 games under .500 at 59-71 and 13 games behind Chicago, but on nights like this, it’s easy to imagine better times.

“The White Sox and Tigers,” Francoeur said, “those are two good teams. They’re going to be battling it out. But this might have been one of the best three-game series, baseball-wise, that we’ve played. Three one-run games.”

Guthrie scattered eight hits through the first seven innings, but the Tigers put the tying run on base in the eighth with one-out singles by Fielder and Delmon Young.

That prompted changes.

The Royals went to the bullpen for Collins, while Quintin Berry replaced Young as a pinch runner. The Tigers also sent up Jeff Baker to bat for Brennan Boesch to avoid a left-on-left matchup against Collins.

Baker struck out on three pitches, but Jhonny Peralta grounded an RBI single up the middle on a full count. That broke an 18-inning scoreless streak for the Tigers.

Crow replaced Collins, and Crow stranded two runners by retiring Omar Infante on a fly to center. The run was charged to Guthrie, who allowed one run and 10 hits in 7 1/3 innings.

But all that was mere prelude to the ninth with Cain’s catch and Escobar’s showstopper.

“It was nothing new with Esky,” first baseman Eric Hosmer said. “Nothing ever surprises you. There’s a name for that play, but I don’t know what to call it.”

Detroit starter Rick Porcello, 9-10, allowed two runs and eight hits in five-plus innings.

“It was one of those freak nights,” Tigers manager Jim Leyland said. “You look up and see 12 hits, but we only scored one run and you wonder what happened.”

The game was scoreless into the Royals’ fifth, which Moustakas started with a double into the right-center gap. Francoeur followed by snapping a zero-for-19 skid with a line single to center.

Third-base coach Eddie Rodriguez chose to stop Moustakas at third with no outs. A wild pitch by Porcello moved Francoeur to second, but Moustakas chose to stay at third.

A walk to Hosmer loaded the bases for Giavotella, who produced a run on a fielder’s-choice grounder to short. Porcello limited the damage to that one run by striking out Cain and retiring Escobar on a sharp grounder back to the mound.

The Tigers had a chance to answer in the sixth after catching a break when Francoeur took a poor route to Fielder’s leadoff liner. The result was a double, but Guthrie pitched around the threat.

Young grounded out to third. Boesch flied out to medium center. And Peralta grounded out to second.

All in a span of four pitches.

Gordon then opened the Royals’ sixth with a homer – a 391-foot drive to right that just cleared the wall above a leaping Boesch. That proved to be the winning run.

“Spectacular pitching again by Jeremy Guthrie and great defense,” manager Ned Yost said. “That’s a huge double play to end the ballgame right there. We had a couple opportunities to add on, but two runs were enough.”