SEATTLE -- Even when Corey Kluber isn't at his best, he is more than good enough for the hot-hitting Cleveland Indians.

The reigning American League Cy Young Award winner struck out 13 batters Thursday night but also gave up a season-high two home runs. Thanks to Cleveland's a big early lead, he did enough to extend his winning streak to three consecutive decisions in a 5-3 victory over the Seattle Mariners.

"Everybody's just hitting," Indians first baseman Brandon Moss said after his home run and single were among Cleveland's 10 hits. "Obviously, our pitching has been incredible; that goes without saying. Offensively, guys are starting to get into their groove."

Cleveland (22-25) had a three-run fourth inning on the way to a 5-1 lead, but home runs by catcher Mike Zunino and left fielder Dustin Ackley kept the Mariners in the game. Ackley's two-out, two-run homer in the sixth brought Seattle within 5-3, but the Mariners managed only one hit the rest of the way.

Kluber (3-5) increased his strikeout total over his past four starts to 50. He allowed three runs on seven hits over seven innings. He hadn't allowed a home run since May 7 and had given up just two in five previous starts this month before Zunino and Ackley took him deep Thursday.

"He does a really good job of pitching to the score," Moss said of Kluber. "It's fun to watch him, that's for sure."

Seattle starter James Paxton (3-3) came out after 83 pitches because of what the Mariners called discomfort in the middle finger of his pitching hand. The left-hander allowed eight hits and four runs (three earned) in 4 2/3 innings. Paxton will be re-evaluated Friday, and he is expected to undergo X-rays.

Seattle manager Lloyd McClendon said after the game that Paxton didn't feel any discomfort before his final pitch.

"As of right now, I don't know," McClendon said of the injury. "We'll know more (Friday)."

Cleveland improved to 8-2 since May 19. The Indians' No. 7, 8 and 9 hitters went 5-for-10 and scored five runs.

"We made (Paxton) work hard," manager Terry Francona said, "and we had some runs to show for it."

Closer Cody Allen earned his 10th save of the season after pitching a scoreless ninth, which included a pinch-hit appearance by Mariners second baseman Robinson Cano. Seattle's usual No. 3 hitter was out of the starting lineup for the first time this season due to flu-like symptoms.

Seattle (23-24) was trying to go above .500 for the first time since winning on Opening Day, but it had its three-game winning streak snapped. The Mariners went 0-for-3 with three strikeouts with runners in scoring position. Most of Seattle's production came from the bottom of the order, as designated hitter Nelson Cruz and third baseman Kyle Seager combined for five strikeouts.

"As the season progresses, we're going to have to have production from the bottom of the lineup," McClendon said. "It was good today, and we needed that."

The last time Kluber gave up more than one home run in a game was Sept. 1, 2014, when the Tigers took him deep three times in Detroit's 12-1 win over the Indians.

The Indians used a three-run fourth to jump out to a 4-1 lead off Paxton.

Three singles, a walk and an error on Mariners shortstop Chris Taylor opened the door for Cleveland's red-hot offense to break a 1-1 tie and eventually score three runs in the fourth.

"Anytime the offense can give you that kind of run support, it's always nice," Kluber said. "I made a mistake to Ackley (in the sixth), and having that kind of lead helped."

NOTES: Mariners 2B Robinson Cano (flu-like symptoms) was held out of the starting lineup for the first time this season, though he pinch-hit in the ninth and flied out. Manager Lloyd McClendon said pregame that Cano received intravenous fluids for dehydration since playing in Wednesday's game at Tam