ST. PETERSBURG, Fla. (AP) -- Corey Kluber appreciated Austin Jackson's efforts, both with the bat and glove.
Jackson led off the eighth inning with a home run, sending Kluber and the AL Central-leading Cleveland Indians over the Tampa Bay Rays 4-3 on Sunday.
"He's been a huge part of this team so far and it's both offensively and defensively," Kluber said. "He's shown when he's healthy he's still got a lot left."
Jackson also ran down a line drive to left field by Corey Dickerson in the first inning that could have gone for extra bases.
"We talk so much about being ready for the first inning," Cleveland manager Terry Francona said. "That can change the game because he's ready to go full tilt. If not, that's a double."
Kluber (11-3) struck out nine in seven innings, his 14th straight start of fanning eight or more. He gave up four hits, including a two-run homer to Steven Souza Jr. that made it 3-all.
Kluber is 8-1 with a 1.85 ERA in those 14 starts since coming off the disabled list. It wasn't his best game, but it was good enough.
"Throughout the course of the season you have days where you feel good and days where you don't," he said. "So you've got to try to manage it."
Cody Allen pitched the ninth for his 21st save.
The Rays went 2-7 on a nine-game homestand in which they were shut out five times and scored only 11 runs.
Jackson's fourth homer accounted for only the second run given up by Tommy Hunter (2-3) in his last 21 appearances.
Jay Bruce and Carlos Santana hit RBI doubles in the fourth off Austin Pruitt that put the Indians up 2-1. Edwin Encarnacion added his 24th homer in the sixth.
The Rays put together three hits off Kluber, including Evan Longoria's RBI single, to take a 1-0 lead in the third.
Souza's 25th homer tied it in the sixth after Kluber walked Longoria.
"It's a step in the right direction that we got going a little bit," said Souza. who also stole a base and threw out a runner at the plate.
"Anytime you face Corey Kluber, you know you're not going to score nine runs, so I thought the way we went after him was pretty impressive. We battled to the very end," he said.
Pruitt gave up three runs on four hits in six innings in his third straight start against an All-Star pitcher.
The Rays hit just .170 and struck out 100 times in their homestand, which opened with 19 straight scoreless innings against Milwaukee. Tampa Bay had gone 20 innings without scoring until touching Kluber.
"Maybe it's a good thing we're out of here for four days and heading to Toronto," manager Kevin Cash said.
Indians: LHP Andrew Miller (knee tendinitis) felt good after throwing a morning bullpen session. The Indians have yet to determine whether he will need a rehab appearance before being activated.
Rays: RHP Matt Andriese (right hip stress fracture) gave up two runs on four hits in three innings in his first rehab start for Class A Charlotte, his first appearance since June 10.
Indians: RHP Trevor Bauer (10-8) will pitch against RHP Doug Fister (2-5) of the Red Sox on Monday night in Boston in a makeup of a rainout on Aug. 2.
Rays: RHP Jake Odorizzi (6-5) will face RHP Nick Tepesch (0-2) on Monday night in the first game of a four-game series in Toronto.