KANSAS CITY, Mo. — The Detroit Tigers fell behind by four runs on a grand slam by Kansas City Royals superstar Bobby Witt Jr. in the third inning, but they chipped away at the deficit in the middle innings.

The never-quit Tigers scored one run in the fourth, three runs in the fifth and three runs in the sixth. Along the way, the Tigers received key hits from Colt Keith, Wenceel Pérez and Matt Vierling, among others.

"I don't think anybody thought we were out of it," Keith said.

The Tigers beat the Royals, 7-6, in Monday's opener of a three-game series at Kauffman Stadium.

With the win, the Tigers (78-73) trail the Minnesota Twins by 1½ games for the third and final spot in the American League wild card, with 11 games remaining. The Twins blew a three-run lead in a 4-3 loss to the Cleveland Guardians in the first of four games in their series.

The Tigers have a 23-10 record in their last 33 games.

"Huge win," manager A.J. Hinch said. "It was an incredible win because of how we had to do it. ... Incredible win and great performance by so many of our guys."

To get to the finish line, the Tigers had to keep the Royals from scoring in the final four innings after grabbing a 7-6 lead in the sixth inning. They were successful in doing so, thanks to strong performances from relievers Brenan Hanifee, Will Vest, Beau Brieske and Jason Foley.

In the seventh, Vest stranded runners on the corners when he recorded flyouts against both Witt and Salvador Perez. In the eighth, Brieske stranded runners on first and second when he struck out MJ Melendez and induced an inning-ending double play against Maikel Garcia.

Brieske struck out Melendez with a 99.5 mph fastball.

"A couple different times they responded to us scoring by getting guys on base," Hinch said. "It's a ton of pressure. They run a lot. They have a lot of athleticism. There's a reason why these guys have a ton of wins, and why they're in the thick of things. They play their 27 outs, too."

Foley took over for the ninth inning.

He retired pinch-hitter Robbie Grossman, Kyle Isbel and Tommy Pham in order for his 24th save in 27 chances.

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Reese Olson returns

Right-hander Reese Olson returned from a near two-month absence on the injured list. The 25-year-old hadn't pitched for the Tigers since July 20 because of a right shoulder strain.

He retired six batters in a row, a product of his nasty slider, before walking Adam Frazier to open the third inning.

"I felt fine," Olson said. "That's a win, I guess. The first two innings, I felt about as good as I could. In the third inning, I walked a guy, ground ball finds a hole, the bunt, and then I made one bad pitch. It's four runs, but the guys picked me up."

The Royals loaded the bases in the third, thanks to Frazier's walk, Yuli Gurriel's single that got past shortstop Trey Sweeney, and Isbel's perfect bunt single.

Witt took advantage by crushing Olson's hanging curveball for a grand slam — putting the Royals ahead, 4-0 — with one out in the third inning. After that, Perez slapped a single to right field that chased Olson from his start.

Olson allowed four runs on four hits and one walk with three strikeouts across 2⅓ innings, throwing 50 pitches. He generated five whiffs on 18 swings, but all five whiffs were from sliders.

Rally Tigers

The Tigers stranded the bases loaded in the third inning, when Keith grounded out, but the Tigers didn't miss later opportunities to score against right-hander Seth Lugo.

Sweeney delivered a sacrifice fly in the fourth inning, cutting the Tigers' deficit to 4-1. The Royals answered with a run against left-handed reliever Sean Guenther in the bottom of the fourth.

In the fifth inning, Vierling hit an RBI single and Keith crushed a two-run home run, making it a 5-4 deficit.

Keith pulled Lugo's first-pitch changeup for a two-run home run to right-center field. It was his 13th homer in 138 games but his first homer since Aug. 24 (and his second homer since July 27).

"I thought he was going to throw a first-pitch fastball," Keith said, "and I wanted to hit it to center and get the barrel out on it. He ended up throwing a changeup, left it in the zone, and I just tried to stay through it as best I could. I ended up back-spinning it, so that got it out of the park."

Lugo allowed four runs on eight hits and two walks with four strikeouts across 4⅔ innings, throwing 96 pitches. He entered Monday's game with a 2.94 ERA but departed with a 3.05 ERA following his 31st start.

The Tigers worked Lugo for 64 pitches in the first three innings, including 24 pitches in both the first and third.

"It's nothing overpowering," Spencer Torkelson said. "It's not like it's 98 (mph) where you don't see it. It's really an at-bat where you get yourself out early if you let him. You know he's not going to give in. It's being selective, but not too selective. It's like a semi-selective aggressive approach."

Again, the Royals responded with another run — taking a 6-4 lead — on Isbel's triple and Witt's infield single against Hanifee in the bottom of the fifth.

The Tigers, though, wouldn't go away.

Back-to-back singles from Andy Ibáñez and Jake Rogers against left-handed reliever Sam Long put runners on the corners in the sixth inning, with Pérez driving them in on a pinch-hit, two-run double into the left-field corner. After that, Vierling shot an RBI single into right field, facing right-handed reliever John Schreiber.

The three-run sixth put the Tigers ahead, 7-6.

"He's a guy that was hitting in the middle of our order, gets hurt (with an oblique strain), and when he comes back, everything on our team has changed, and he didn't change," Hinch said of Pérez. "He hasn't missed a beat. We hurried him back to get him in the mix because having a switch-hitter, even if it was on the bench, is going to be very valuable to make decisions during the game."

Contact Evan Petzold at epetzold@freepress.com or follow him @EvanPetzold.

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This article originally appeared on Detroit Free Press: Detroit Tigers inch closer to playoffs with 7-6 win vs Royals