KANSAS CITY, Mo. -- While Danny Salazar has the Royals' number, Kansas City continues its search for a dependable No. 5 starter.

Salazar pitched effectively into the seventh inning, and Mike Napoli and Francisco Lindor homered as the Cleveland Indians defeated the Royals 7-3 Tuesday night.

Salazar (11-3) gave up three runs, two earned, on eight hits and a walk in 6 1/3 innings. He struck out seven.

The All-Star right-hander is 3-0 with a 1.21 ERA in three starts this season against the World Series champion Royals, having allowed 15 hits while striking out 25 in 22 1/3 innings.

"The All-Star break was a really good break for me," said Salazar, who pitched Tuesday on nine days' rest. "I went to the All-Star Game and really didn't do much besides play catch. My elbow felt fine tonight."

The Indians, whose 55-38 record is the best in the American League, picked up a game in the AL Central standings on the second-place Tigers, who lost to the last-place Minnesota Twins. Detroit is 6 1/2 games back, and the Royals fell eight games behind.

Salazar did not give up a run until the sixth. With one out, Eric Hosmer, Kendrys Morales and Salvador Perez singled. Hosmer scored on Perez's ground-ball hit. Morales scored the second run of the inning on a Salazar wild pitch.

Salazar gave up an unearned run in the seventh, which began with a Whit Merrifield walk and a Jarrod Dyson single. Both runners moved up on a passed ball charged to Chris Gimenez. Cheslor Cuthbert's sacrifice fly to left scored Merrifield. Left-hander Kyle Crockett, who was called up Monday from Triple-A Columbus, relieved Salazar and struck out Hosmer on five pitches to end the inning.

"Danny did a really good job and kept them off the scoreboard for the most part," Indians manager Terry Francona said. "Like I said, we needed a bounce back win."

Lindor, who is hitting .444 with four home runs, 10 RBIs and 11 runs this season against the Royals, homered in the ninth. Lindor went 2-for-4 with a sacrifice fly and scored three runs.

"I'm just real impressed," Royals manager Ned Yost said of Lindor. "He's just a fantastically talented young man on both sides of the ball, offensively and defensively. He's just good."

Indians reliever Bryan Shaw, who took the loss Monday when he was charged with four runs in two-thirds of an inning, threw eight pitches, all strikes, in a 1-2-3 eighth inning. He struck out Morales and Perez on six pitches before retiring Alex Gordon on a comebacker.

"It felt good to have a good bounce-back inning after Monday," Shaw said. "I went out there and tried to forget what happened Monday, throw strikes and get ahead of guys. When I get ahead of guys, it is a lot better outcome than when I don't."

Cody Allen closed out the win with a perfect ninth inning.

The Royals turned to left-hander Brian Flynn to attempt to fill the void of a reliable No. 5 starter. However, Flynn, who was making his first start since Aug. 7, 2014, with the Marlins, did not make it through the third inning.

"We're just looking for a guy right now," Yost said to fill that final rotation slot. "We've got time to think about it. We've got an off day on Thursday, so we'll be able to skip that spot the next time around. We'll probably take advantage of that and consider all of our options."

Flynn (1-1) yielded three runs, four hits and a walk while striking out one in 2 1/3 innings. He was replaced by Dillon Gee after only 43 pitches, 28 of them strikes.

Flynn yielded a two-run homer to Napoli, who hit his 21st of the season with two outs in the first with Lindor aboard. Napoli has four home runs in 2016 against the Royals and 14 in his career.

"I was just trying to bust him in there, knowing he was going to be swinging 2-and-0, trying to get in and get in a soft ground ball," Flynn said. "I just tried to get it in, saw him off or try to get weak contact, but it stayed right over the middle. Really, that was the pitch that hurt me tonight. Three of the four hits were four-seamers we were trying to get in."

The Indians loaded the bases in the third with no outs. Erik Gonzalez opened with a single, his first major league hit. After Flynn walked Rajai Davis, Jason Kipnis put down a sacrifice bunt that Salvador Perez picked up. Perez threw to third in an attempt to get the lead runner, but Gonzalez beat the throw. Lindor's sacrifice fly to Paulo Orlando scored Gonzalez and finished Flynn's night.

The Indians made it 6-0 with a three-run fifth against Gee. Carlos Santana's bases-loaded, one-out single to right scored Kipnis and Lindor. Kipnis doubled and moved to third on Lindor's single, and Napoli worked a walk to load the bases. Juan Uribe's two-out single brought Napoli home.

NOTES: Indians LF Michael Brantley is still feeling shoulder discomfort when he completes his swing, and he will have a MRI exam Wednesday. Brantley, on the disabled list since mid-May, has appeared in only 11 games this season because of the aching shoulder. ... Royals 3B Cheslor Cuthbert batted second for the first time this season, becoming the 10th player used by manager Ned Yost in that slot. ... RHP Kyle Zimmer, the Royals' top pitching prospect, will undergo shoulder surgery, a thoracic outlet syndrome procedure. He pitched just 5 2/3 innings in the minors this season. ... Royals LHP Mike Minor, who remains on the 60-day disabled list while recovering from 2015 shoulder surgery, threw 36 pitches in a two-inning simulated game. ... Indians RHP Carlos Carrasco and Royals RHP Ian Kennedy are the pitching probables Wednesday for the series finale.