NEW YORK -- The Rays had their chances Tuesday night. They were a few errors in the field away from shutting out the Majors’ most dangerous lineup. They were a few timely hits -- and perhaps one key replay review -- away from breaking through against the Yankees’ ace.

But they came up short at every turn, and those missed opportunities loomed large in a 2-0 defeat at Yankee Stadium. By dropping the first of their six matchups in a nine-day span, the third-place Rays (35-26) fell a season-high 10 games behind the Yankees (45-16) in the American League East standings.

The way the Yankees have been dominating opponents so far this season, the Rays knew heading into this series they’d have their work cut out for them over these three days in the Bronx and again in a three-game series at Tropicana Field next week. With so little margin for error, they were reminded in the opener, every moment matters.

“I thought we played well,” Rays manager Kevin Cash said afterward. “I mean, we didn't hit, and two plays that we normally convert into outs -- or one, for sure -- we didn't. And that was the outcome of the ballgame.”

It was indeed a close and competitive game, thanks in large part to another strong start by Corey Kluber. The veteran right-hander held New York’s homer-happy lineup to four hits and a walk while striking out three over six innings, but the Yankees gained the upper hand in the fourth thanks to some uncharacteristically sloppy defense by the Rays.

With one out and Giancarlo Stanton on first base, Kluber got Gleyber Torres to hit a fly ball to right field. Manuel Margot looked to have an easy play in front of him, but the ball kicked off his glove, allowing Torres to reach safely and Stanton to move up a base. Kluber noted the play was “probably tougher than it appears” due to the wind, but the sure-handed Margot made no excuses for his rare error and said he thought he had the ball the whole way.

“I don't really have an explanation for it,” Margot said through interpreter Manny Navarro. “When I was about to catch it, I don't know if I just closed the glove a little bit earlier, but I didn't get it.”

Kluber struck out Matt Carpenter, which would have ended the inning had Margot caught Torres’ fly ball. Instead, with two outs, Isiah Kiner-Falefa lined an 0-2 pitch from Kluber into left field. A good throw would have made for a close play at the plate, but Randy Arozarena sailed the ball way over leaping catcher Francisco Mejía. Stanton easily scored the game’s first run.

Kluber shouldered some of the blame for the second run, acknowledging he was a little late backing up the play at the plate after watching to see if Arozarena would catch the ball. Kluber retrieved the ball and tossed it to Mejía, but Torres slid home safely to make it a 2-0 game.

“You hate to see an outcome of a game turn that way, but at that point, that was a pretty big couple moments right there,” Cash said. “I thought Corey was outstanding.”

But the Rays couldn’t support Kluber at the plate, either. They managed just one hit while striking out six times through four innings against Gerrit Cole -- who pounded pitches away from Tampa Bay’s hitters all night -- then whiffed on scoring opportunities in Cole’s final two frames.

Arozarena singled and Kevin Kiermaier walked to put two runners on with nobody out in the fifth, but Cole settled down and retired Isaac Paredes, Mejía and Taylor Walls in order. The Rays let an even better chance in the sixth go to waste, although they felt a replay review played a big part in stalling that rally.

Yandy Díaz hit a leadoff single and seemingly advanced to second on a throwing error by Cole, who had fielded Harold Ramirez’s comebacker. Nobody on the field, not even Cole, initially thought Díaz was out. But the Yankees challenged the call, believing the tip of Torres’ cleat was touching the bag when he caught the ball, and it was ultimately overturned. Díaz did not hide his disagreement.

“I thought it was a bad call, and I think it cost us the game,” Díaz said through Navarro. “I think it was a surprise. I think a 5-year-old would have been able to see that I was safe at second.”

Still, the Rays managed to load the bases for Arozarena with one out and Cole seemingly on the ropes. But Cole fired a first-pitch slider below the strike zone that Arozarena said he “just missed” as he grounded into a 6-4-3 double play. The Rays stranded eight runners on the night, were shut out for the fourth time in their last 31 games and scored fewer than four runs for the 28th time in 61 games overall.

“He did a good job. He was locating his pitches really well,” Arozarena said. “We've just got to come back tomorrow with a different attitude and come in ready to play.”