Michael Brantley's first-inning homer held up as the difference as the Indians snapped a nine-game losing streak, sending the Yankees to their fourth defeat in five games.
New York's 3 1/2-game in the American League East remained unchanged as the Rays lost, 4-2, to the Athletics.
"We had our chances," catcher Russell Martin said. "We had the bases loaded a couple times and hit the ball well a couple times. We just didn't get any balls to fall for us."
Masterson wriggled clear of late trouble to limit New York to just one run over 6 2/3 innings, while Vinnie Pestano recorded four outs and Chris Perez locked down the ninth inning for his 33rd save.
"We didn't get the big hit today, but between Masterson and the two relievers they threw out there, it's tough," Mark Teixeira said. "Their eighth- and ninth-inning guys are two of the best in baseball, so it was one of those tough games."
Kuroda had lost just once over his last 11 starts coming into Saturday's action, and his 2.98 ERA ranks sixth in the AL, but he was forced to pitch from behind early.
Trying to slip a 93-mph sinker past Brantley, Kuroda got too much of the plate and served up a three-run homer, Brantley's sixth of the year.
"I was trying to locate the ball outside, and I was being too careful," Kuroda said. "I got behind in the count."
From there, Kuroda settled in and continued his sharp recent run on the mound, working all eight innings for a complete-game loss while limiting the Indians to four hits and two walks, striking out six.
"I didn't think he really had his good stuff most of the night, but he found a way to get people out," manager Joe Girardi said.
Kuroda may not have had his good slider, but he also didn't receive much help from his offense, which may have reminded him of the light-hitting lineups he had behind him during his years with the Dodgers.
New York went 1-for-7 with runners in scoring position, leaving two on in the fifth, then stranded the bases loaded in both the sixth and seventh innings.
In all, the Yankees had 10 runners on base between the fourth and seventh innings, able to bring home only Derek Jeter on Teixeira's sixth-inning sacrifice fly.
A walk loaded the bases again, but Eric Chavez lined out to third base and Martin flied out to deep right field on a nice catch by Shin-Soo Choo.
"They got one, and the goal is to minimize the damage," Masterson said. "We were able to do that, however pretty or not pretty it was. We got through it and made it work."
New York threatened again in the seventh, chasing Masterson with a two-out rally. A walk loaded the bases, but Pestano shattered Teixeira's bat on a harmless popup.
"You always want to reward a pitcher for pitching well, and other than the first inning, Hiro was amazing -- the way he's really been all year," Teixeira said. "It's tough when we can't get him any runs."
Before the game, Girardi said that Kuroda deserves to be in the discussion for the AL Cy Young Award and mentioned that the hurler's won-loss record -- now 12-9 -- could be far better with some more run support.
"He's been pitching so good," Indians manager Manny Acta said. "We saw him in New York in July, and ever since, he has continued to throw the ball very well. Nothing is straight."
Kuroda said that he doesn't want to concern himself with the run-support issue, though when asked if that's easy, he replied, "I try to convince myself."
To be sure, wins and losses aren't the best statistical measure of a pitcher's ability, but a few more victories here and there would certainly permit Kuroda to leave the stadium in a better mood.
"Obviously, [when] you go out there on the mound, you try to win," Kuroda said. "If that doesn't happen, it's not a really good feeling. I try not to dwell on it and regroup myself. I'll be ready for the next start."