NEW YORK -- Nobody needs to remind the New York Yankees that Corey Kluber's foot has been exceptional for almost three months.

Kluber won a battle of the aces Monday night when he outdueled Yankees right-hander Luis Severino by allowing three hits in eight impressive innings in the Cleveland Indians' 6-2 victory.

Cleveland took the opener of a three-game series at Yankee Stadium.

Kluber (13-4) allowed two runs and one walk while striking out seven. He is 10-2 with a 1.90 ERA in 17 starts since being activated from the disabled list on June 1.

"I think everybody's goal is to try to consistently do well and give the team a chance to win as a starting pitcher," Kluber said. "My opinion is that just because you get on a good stretch, you don't take your foot off the gas pedal. If anything, work harder to try to continue to do that."

The strong outing Monday marked the fifth time since returning to the active roster that Kluber has thrown at least eight innings and allowed three hits or fewer. The only team he has done that twice against is the Yankees, who mustered just three hits in a complete game by Kluber on Aug. 3 when the Indians cruised to a 5-1 win.

"Everybody knows that Kluber is a really good pitcher," Yankees catcher Gary Sanchez said through an interpreter. "He executes all his pitches, and he throws a lot of strikes. He's a tough pitcher to hit off."

The matchup between Kluber and Severino, who began the day ranked first and third in the American League in ERA and third and fourth in strikeouts, lived up to expectations. In the first four innings, both pitchers allowed only one hit -- Severino surrendered a homer to Jose Ramirez in the first, and Kluber gave up a homer to Chase Headley in the third.

"You can't help but be aware of who's pitching for the other team," Kluber said, "If it is a guy like Severino, most likely they're not going to give up a lot of runs."

The Yankees took a 2-1 lead in the fifth when Jacoby Ellsbury doubled with two outs and scored on Todd Frazier's single. however, Ramirez tied the score by going deep again in the sixth for the Indians' second hit.

"The way their guy was throwing, thank goodness Jose had the two homers to kind of get us even," Indians manager Terry Francona said.

The Yankees produced just one more baserunner -- Kluber walked Aaron Hicks leading off the sixth -- the rest of the way.

The Indians took the lead in the seventh. Carlos Santana homered with one out for a 3-2 advantage. Bradley Zimmer added a run by singling, stealing second, advancing to third when second baseman Starlin Castro dropped the ball and scoring on a wild pitch by Adam Warren.

Staked to the two-run lead, Kluber set the Yankees down in order in the seventh on just nine pitches.

"The shutdown inning is so important, and sometimes not just shutting them down, but it's the way you shut them down," Francona said. "Come out and (the pitcher is) aggressive and hopefully it takes maybe the starch out of (the opponent) a little bit."

Zimmer added an RBI double in the ninth for the Indians (74-56), who have won five straight, during which they have outscored the opposition 39-8. Cleveland extended its lead in the AL Central to a season-high seven games over the idle second-place Minnesota Twins.

Cody Allen tossed a perfect ninth in a non-save situation.

"It was two really good pitchers going at it," Francona said. "Fortunately, Kluber stayed the course, did what he usually does."

Severino (11-6) allowed four runs (three earned), four hits and three walks while striking out nine in 6 2/3 innings.

"That's how Kluber's going," Yankees manager Joe Girardi said. "He's not giving up many runs every time he goes out there, and the few mistakes cost (Severino)."

The Yankees (70-60), who were limited to three hits or fewer for just the fourth time this season, fell 3 1/2 games behind the AL East-leading Boston Red Sox. New York leads the Twins by three games in the race for the first AL wild card.

NOTES: Yankees RF Aaron Judge didn't play and may also sit out Tuesday. Manager Joe Girardi acknowledged Judge has been icing his shoulders after games lately but said the rest was more to allow Judge to clear his head. The rookie is batting .179 with 65 strikeouts in 145 at-bats since the All-Star break. ... Girardi said Yankees DH Matt Holliday (back) may soon move his rehab assignment to Triple-A Scranton/Wilkes-Barre. ... Cleveland OF Abraham Almonte (left hamstring) went 1-for-3 in his first rehab game for Triple-A Columbus. ... Indians RHP Danny Salazar (right elbow) threw on flat ground and is scheduled for a bullpen session on Tuesday.