St. Petersburg, Fla. ? Mike Moustakas and the Kansas City Royals both kept up their strong play.

Moustakas had three hits and three RBIs, Kendrys Morales came through with another big two-out hit, and the AL Central-leading Royals beat the Tampa Bay Rays, 6-3, on Saturday night.

Moustakas has driven in 15 runs over his last 10 games. The Royals have won 17 of 22 to go a season-high 31 games over .500 (80-49).

“You wouldn’t know that we’re 31 games over .500,” Moustakas said. “We come in expecting to win every night. We come in to grind it out, play the game hard. That’s what we’re doing, and it translates on the field.”

Morales had an RBI single and Moustakas a run-scoring double off Jake Odorizzi (6-7) as the Royals grabbed a 4-3 lead in the fifth. Morales leads the majors with 47 RBIs with two outs this season, breaking the team record of 46 set by Joe Randa in 2000.

Lorenzo Cain had a run-scoring single in the sixth, and Moustakas added an RBI single in the ninth.

“He’s using the whole field, which is impressive,” Royals manager Ned Yost said of Moustakas. “Really swinging the bat well.”

Kris Medlen (3-0) allowed three runs and four hits over 5 1/3 innings in his second start and ninth appearance since returning from elbow ligament replacement surgery. Wade Davis, the third Royals reliever, recorded the last three outs for his 13th save.

Kevin Kiermaier homered for the Rays, who have lost 10 of 15. Tampa Bay has dropped all six games against Kansas City this season and 20 of 25 over the last four seasons.

“They look like a playoff team and I think our guys know that,” Rays manager Kevin Cash said. “We’re getting a first-hand look at a really good team.”

Tampa Bay took a 3-2 lead in the fourth when Asdrubal Cabrera had a run-scoring single and Kiermaier hit a two-run homer.

Eric Hosmer, mired an 0-for-13 slide, and Moustakas both had RBI doubles during the top of the fourth to put the Royals ahead 2-0.

Odorizzi allowed four runs and seven hits in 4 2/3 innings. He is winless in six starts, which includes a stretch of five no-decisions where the right-hander pitched at least six innings in each game.

Rays catcher Rene Rivera got cut on the lower lip after Medlen’s pitch deflected off Rivera’s arm and struck his face in the third. After a brief treatment period with a team trainer near the plate, Rivera remained in the game and went to first base.

Tampa Bay loaded the bases with two outs later in the third, but failed to score when Evan Longoria struck out.

The Rays became the last team in the majors to reach 1 million in home attendance with an announced crowd of 24,372.

Trainer’s room

Royals: Yost said LF Alex Gordon, out since July 9 with a strained left groin, is getting close to returning. Gordon is currently on a minor-league rehab assignment with Triple-A Omaha. … OF Alex Rios was a late scratch due to illness.

Rays: LHP Matt Moore should get some starts after rejoining the team next month. He was sent to Triple-A Durham Aug. 3 after going 1-3 with an 8.78 ERA in six starts following his return from elbow ligament replacement surgery. “We need Matt to pitch,” Cash said.

Royal control

Kansas City is bidding today to win the season series with the Rays 7-0. Tampa Bay has never gone 0-7 or worse against any opponent in one season. … The Royals have scored 42 runs in the six wins so far this year.

More Morales

Morales is hitting .375 (9 for 24) with eight RBIs against the Rays this season. … His 90 RBIs this year are the most by a Kansas City player since Billy Butler had 107 in 2012.

Up next

Royals LHP Danny Duffy (7-6) will go against Rays RHP Nathan Karns (7-5) in the finale of the three-game series today.