CLEVELAND -- The Royals entered Monday coming off two bad losses to the Phillies at home and sat three games behind the American League Central-leading Guardians with a four-game, three-day series about to begin at Progressive Field.

They ended the first day just one game behind the Guardians following Monday’s doubleheader sweep, emphatically ending the nightcap with a 9-4 win following a 4-3 victory in Game 1.

“You couldn’t ask for any more,” manager Matt Quatraro said. “By no means does that mean anything’s done, but these guys played extremely hard today. After getting beat up the last couple days, put that behind them, came out here and really focused on one game at a time.”

The Royals have a firm hold on an AL Wild Card spot, 1 1/2 games ahead of the Twins for the second spot, with the Red Sox falling five games behind Minnesota as the next closest team. Kansas City is now 6-2 against Cleveland this year and can clinch the season series with one more win in the final five games.

And it’s the division Kansas City wants. With seven games in 10 days against Cleveland, a sweep on Monday was as good of a way to begin this division-implicating stretch in the schedule.

A grand way.

Salvador Perez mashed two home runs in back-to-back innings, including a grand slam in the sixth inning. Perez’s 17 multihomer games and six grand slams tie George Brett and Frank White, respectively, for most in franchise history.

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Perez is the only Royal remaining from the 2015 World Series championship team, enduring eight non-contending seasons -- including three 100-plus loss campaigns -- since.

This year, the Royals captain is trying to lead his club back to October. He’s recorded an RBI in six of his last 11 games and has driven in 19 runs in his last 16 games since Aug. 9.

“It’s nothing we can hide, what was going on here last year, two years ago, even six years ago after we won the World Series,” Perez said. “I always tell myself, ‘Hopefully we stop losing because I want to go back to the playoffs.’ Every game is very important to us. And everybody has the same goal, the same mentality here.

“… As soon as you play in the playoffs, you don’t want to play ever again in the regular season. You just want to play in the playoffs.”

Perez’s six RBIs on Monday night set a new career high. And it gave him 94 this year, joining Bobby Witt Jr. and Vinnie Pasquantino with 90-plus RBIs this season. That makes the Royals the first team in the Majors to have three players reach that mark.

Perez’s first home run came a pitch after he foul tipped a sweeper from Guardians starter Logan Allen that home plate umpire John Tumpane said hit the dirt first before catcher Bo Naylor’s glove, giving Perez another chance. The same situation happened two other times Monday night, and Tumpane checked the ball for marks both times.

“That was a foul ball,” Perez said. “I know people were talking about that. But a foul ball is a foul ball. I liked that the umpire checked the ball. It can [go] on the opposite side, it can happen to me when I’m behind the plate catching.”

Perez didn’t miss the next sweeper up and on the outside part of the zone, breaking a tie to mark his 28th go-ahead RBI this year.

An inning later, Perez hit a Statcast-projected 457-foot grand slam to put a back-and-forth game firmly on the Royals’ side. Perez went a combined 5-for-7 with two walks and two homers in the doubleheader Monday.

The 34-year-old Perez admitted he was ready to be the designated hitter by the time Game 2 came around after catching a one-run game in the heat earlier in the day.

“After I caught the first one, I was like, ‘[Freddy] Fermin’s got it,’” Perez said, laughing.

Fermin caught Alec Marsh’s first start back in the Majors after he was optioned to Triple-A Omaha on July 31. The righty starter overcame a bad defensive first inning when right fielder Dairon Blanco badly misplayed a fly ball, leading to two runs, and Marsh allowed another run on an errant pickoff throw.

He settled down to get through 4 2/3 innings, and the Royals offense got to work on the comeback, including contributions from Paul DeJong (solo homer) and Maikel Garcia (3-for-4, RBI, two runs scored). Daniel Lynch IV, who was called up earlier Monday, picked up his first career save by pitching three scoreless frames to end it.

“Any time you play a really good team like Cleveland and you get the first two on the first day, it’s pretty good,” Perez said.