CLEVELAND -- Tampa Bay Rays manager Kevin Cash was the Cleveland Indians' bullpen coach in 2014, the year Corey Kluber won the Cy Young Award, so he's seen this before.

"He's pretty good, to say the least, and he had it all going tonight," said Cash after Kluber took a one-hitter into the ninth inning, and finished with a three-hit complete game shutout as the Indians beat Tampa Bay 6-0 Tuesday night at Progressive Field.

Kluber (7-7) struck out nine and walked two in pitching his third career shutout. The only hits allowed by Kluber were singles, by Corey Dickerson in the second inning and by Brad Miller and Evan Longoria in the ninth.

Jose Ramirez had two hits, including a home run, and two RBI and Juan Uribe also homered for the Indians, but Kluber was the star of the show.

"He pitched in off the plate, then spun his breaking ball. He was very good," said Cleveland manager Terry Francona.

The victory extends the AL Central-leading Indians' winning streak to five in a row. They have also won 10 home games in a row.

"We're playing good baseball now. It's nothing earth shattering," Kluber said. "In all aspects of the game we're playing pretty well. Pitching, hitting and defense. The key to winning is putting together complete games."

Kluber retired the side in the first inning on seven pitches. In a six-inning span from the third through the eighth, Kluber held the Rays hitless and scoreless, retiring 18 of the 20 batters he faced, including 13 in a row at one point.

"He's known for pounding the zone," Cash said. "Not many guys have late action at the top of the zone the way he does. He's good. Really good."

Rays rookie left-hander Blake Snell (1-1), in his third major league start, pitched 6 2/3 innings, giving up three runs, two earned, and seven hits with three strikeouts and three walks.

"Blake really threw well. The way he attacked hitters was very impressive. He's going to be a big part of our future," Cash said.

Leading 2-0, the Indians added an insurance run in the sixth inning. With one out, Ramirez singled to right field. Uribe reached on an error by shortstop Miller, moving Ramirez to second. Lonnie Chisenhall followed with a single to center, scoring Ramirez and extending the Cleveland lead to 3-0.

In the eighth inning Mike Napoli led off with a single off reliever Steve Geltz. Ramirez then belted his fourth home run into the seats in right field to push the lead to 5-0.

Uribe, the next batter, hit one over the left-field wall for his sixth home run. Uribe has hit home runs in each of the last four games. He is the first Indians player to homer in four consecutive games since Jason Kipnis did it from July 31-August 3, 2011.

The Indians took a 2-0 lead in the third inning. With Yan Gomes at second and two outs Jason Kipnis hit a line drive to center field that took a bad hop past center fielder Desmond Jennings and rolled all the way to the wall. Gomes scored, and so did Kipnis, sliding head first across home plate.

It was ruled a single and a three-base error, and it gave Cleveland a 2-0 lead.

"That was like the perfect storm. It was like icing in hockey, no one's there. It took a weird hop. I thought they could have given him a home run," Francona said.

"The ball probably hit a sprinkler head," Cash said. "There's not much D.J. can do there. That's very unfortunate."

NOTES: Indians OF Michael Brantley underwent an MRI and was diagnosed with right biceps tendinitis on Tuesday. He was given a cortisone shot. Brantley played in 11 games and made two trips to the disabled list this season following offseason surgery on his right shoulder. He felt discomfort recently in the shoulder, prompting the MRI. There is no timetable for his return. ... Indians 3B Juan Uribe hit just two home runs in his first 48 games, but has hit four home runs in his last four games, including a solo shot in the eighth inning Monday. ... The Rays placed OF Mikie Mahtook (fractured left hand) and UTL Steve Pearce (strained right hamstring) on the disabled list. To replace Mahtook and Pearce on the roster, the Rays recalled INF/OF Nick Franklin and RHP Ryan Garton from Triple-A Durham. Mahtook becomes the fourth Rays outfielder on the DL, joining Brandon Guyer, Steven Souza Jr. and Kevin Kiermaier. ... In the first 40 days of the season, Tampa Bay had no players on the DL. In 37 days since then the Rays have placed eight players on the DL.