AL Central-leading Cleveland won for the fourth time in five games, and then finalized a trade for 2015 AL MVP Josh Donaldson. The Indians sent a player to be named to the Blue Jays for cash considerations and Donaldson, a slugging third baseman who has been limited to 36 games this season because of injuries.
Kluber (17-7) allowed two singles, struck out eight and walked two in Cleveland's AL-best 14th shutout this season. Cody Allen worked a perfect eighth and Brad Hand finished the two-hitter for his 31st save.
It was an encouraging outing for Allen, who lost the closer job during a tough August.
"Just because Cody ran into a hiccup there, we never lost confidence in him," Kluber said. "He's not one of the best closers that we've had in this organization for no reason. We all have the same goal here and that's to win. I thought he looked real good tonight."
Pitching for the third straight day, Allen helped the Indians retire the last 17 batters. He was 0-2 with two blown saves and an 11.57 ERA in his previous six appearances.
"This is a special group we've got and these guys are my bros," Allen said. "I'm not surprised the way they've stayed behind me and picked me up. We've got very, very high character guys who care a great deal about each other."
Kluber, making a bid for a second straight AL Cy Young Award, matched Yankees ace Luis Severino for the major league lead in wins. He also moved into first place in the AL with 186 2/3 innings.
"I thought Klubes was really crisp and I thought Cody looked tremendous," Cleveland manager Terry Francona said. "Cody should feel really good. He should because he's worked hard. Now, we've got to keep him there."
Encarnacion snapped a scoreless tie with a solo drive to center off Tyler Glasnow (1-4) in the seventh. The Indians added two more in the ninth when Greg Allen scored on a wild pitch and Michael Brantley singled home Francisco Lindor.
Glasnow struck out six in a career-high seven innings. He was working on a no-hitter before Melky Cabrera singled with two out in the fifth.
"I was really impressed with the way Tyler threw the ball," Tampa Bay manager Kevin Cash said. "He was just awesome to watch and went toe to toe with arguably one of the best in the game. We couldn't get anything done offensively, but Kluber's numbers speak for themselves."
Francona and Cash are close friends who enjoy kidding each other. Cash fired the opening volley by stealing Francona's dugout chair before the game. Francona responded with a scoreboard graphic entitled "How bad is Kevin Cash at the plate?" that featured his statistics.
Rays: C Michael Perez was placed on the disabled list with a strained left hamstring. ... OF Mallex Smith (viral infection) begins a rehabilitation assignment Saturday with Single-A Charlotte. Smith fell ill and was hospitalized last week. Cash said the leadoff hitter could be activated when he is eligible on Monday.
Indians: RHP Trevor Bauer (right fibula stress fracture) underwent a second bone scan and will learn the results Saturday. The All-Star was struck by a line drive on Aug. 11 and is expected to be out until mid-September.
Rays LHP Blake Snell (16-5, 2.05 ERA) takes on Indians RHP Shane Bieber (8-2, 4.52 ERA) in the second game of the series. Snell is tied for third in the majors in victories behind Severino and Kluber.
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