ST. PETERSBURG, Fla. -- For the third time in as many wins this season, the Tampa Bay Rays waited until the eighth inning to get their bats going.

As he did a week earlier to beat the Toronto Blue Jays, Logan Forsythe hit a two-run home run in the eighth, sparking the Rays to a 5-1 win over Corey Kluber and the Cleveland Indians at Tropicana Field.

"What says most is that we didn't give in to a really good pitcher on the mound," Rays manager Kevin Cash said after Tampa Bay was held to one hit into the seventh inning by Kluber before tying the game. "He pretty much had his way with us for the better part of seven innings, and we finally got something going."

Forsythe's home run -- on a full count with two outs in a tie game -- gave the Rays another efficient win. They have held the lead at the end of just eight innings out of the 63 they have played, yet they are 3-4 on the season.

"It was nice to be able to battle out there," said Rays starter Matt Moore, who held the Indians to one run on five hits in seven innings. "Just being able to keep us right there with an opportunity to win the game. Corey Kluber, it's a tough day for us, but very happy falling behind and being able to come out of it relatively unharmed."

Evan Longoria added a second two-run home run in the eighth -- again with a full count and two outs -- off reliever Cody Allen.

The Rays got strong pitching from Moore, who gave up a solo home run to Francisco Lindor in the fourth inning but shut things down from there. The Indians didn't have a hit from the fifth inning on.

Tampa Bay reliever Xavier Cedeno (1-0) threw a 1-2-3 eighth inning on 10 pitches. Alex Colome, getting the nod for the ninth, tossed a perfect inning to seal the win, getting a leaping grab from right fielder Steven Souza Jr. at the warning track for the final out.

Cleveland (2-3) dominated the Rays in a four-game sweep at the Trop last season, holding Tampa Bay to six total hits in the first three wins. For seven innings Tuesday, it looked to be more of the same, with Kluber barely allowing baserunners.

"There was no wiggle room," Indians manager Terry Francona said. "For seven innings, (Kluber) made it stand up. That's a hard way to pitch, but we'll take that outing."

The Rays were held to one hit until the seventh inning, when they tied the game with a two-out rally off Kluber.

Corey Dickerson hit a line-drive double just out of the reach of left fielder Jose Ramirez. Dickerson came in to tie the game on a single to left from Desmond Jennings, who picked up his first RBI of the season.

In the eighth, Forsythe's second home run of the season came after Kevin Kiermaier reached on a walk and stole second base.

Runs were hard to come by early, with Kluber and Moore both in control.

Moore wasn't quite as dominant. His only mistake was a blast by Lindor to lead off the fourth that was just out of the reach of a leaping Kiermaier in left-center field. The home run was the first this season for Lindor, who also singled in the first inning.

Cleveland could have had more runs that inning. Mike Napoli singled immediately after Lindor's home run but was thrown out by Jennings trying to tag up from first on a fly to the warning track in left field. Yan Gomes followed with a double off the wall, but the Indians couldn't bring him in.

"Easy velocity -- he's running it up there pretty good," Francona said of Moore's effectiveness. "He's back a year removed from Tommy John, and you can see it coming back."

NOTES: Tuesday's game featured two teams grateful to be playing indoors. The Indians had three games postponed already this season, and the Rays had one scrapped Saturday, with off days Thursday and Monday, giving them just two games in a span of five days. ... Tampa Bay scored only 18 runs in its first six games. The Rays were hitting only .205 with runners in scoring position before Tuesday, and of the 39 runners they left on base, 25 were in scoring position. The Rays went 2-for-2 with runners in scoring position Tuesday. ... Cleveland likely will face four consecutive left-handers between its last two games against the Chicago White Sox and the Rays' Matt Moore and Drew Smyly. ... Not only has the weather limited the Indians to four games in nine days, but they were only able to take pregame batting practice outdoors once.