"It was a close game all along, so I had to be careful with my pitches," Kuroda said through an interpreter. "When they gave me the run support, I think I was able to be more bold."
Brett Gardner, Lyle Overbay and Eduardo Nunez each had three hits for the Yankees, who snapped a three-game losing streak to improve to 3-5 this season against Boston and move back within six games of the division-leading Sox.
"We've just got to give ourselves chances to score runs," Overbay said. "We gave ourselves a lot of chances and we didn't come through every time, but the more chances you get, the more opportunities [for it] to happen."
On a day of unconventional outs, Yankees catcher Chris Stewart made the slickest highlight-reel play in the eighth, reaching into the stands to snare Dustin Pedroia's foul pop, then firing to second base to complete a double play by cutting down Daniel Nava.
"That's really big, especially with [David] Ortiz on deck right there as the tying run," Stewart said. "I was just glad I caught it. I saw [Nava] go, so I decided to fire it down there and make it close and we beat it. I don't think I've ever seen it turned. One of those rare things that happened."
But even Stewart's catch and throw, coming after Nava's overaggressive decision to tag up, were arguably surpassed on the scale of extraordinary events in the ninth inning as Mariano Rivera entered to a standing ovation from the largely pro-Red Sox crowd.
Rivera appreciated that warm reception, but it didn't stop him from setting the Red Sox down around a single with two strikeouts, recording his 31st save of the year in 33 opportunities and converting his 12th straight Fenway save dating back to June 3, 2007.
"Definitely, I have tremendous respect for the organization, for the fans here and the field," Rivera said. "Great games. When we come here, it's a battle and beautiful games."
Kuroda pitched six brilliant innings before the Red Sox put up a pair of runs in the seventh, ending his 18-inning scoreless streak. He permitted just one walk, striking out four while hitting a batter.
"[Kuroda] had everything today," Yankees manager Joe Girardi said. "His stuff was really crisp. He kept his pitch count down in the early innings. His stuff was really sharp."
Jonny Gomes had a seventh-inning sacrifice fly and Mike Carp scored on one of Kuroda's two wild pitches to account for the only runs off the veteran, who is 3-3 with a 2.63 ERA in his 10 starts since May 28.
"What was most impressive," Red Sox manager John Farrell said, "was even in that sixth and seventh inning, in these conditions, to be able to reach back and touch 95 and 96 [mph] against the meat of our lineup when he needed that extra velocity, he was able to get it."
Both teams had runners cut down at home plate early. Vernon Wells threw out Nava attempting to score from second base on Ortiz's first-inning single, and Nunez was tagged out as he came home on Luis Cruz's fifth-inning groundout.
The Yankees broke through against John Lackey in the fifth as Gardner stroked a two-out single to center field, scoring Cruz. Boston had another runner gunned down in the fifth on an errant pitch that Stewart tracked down and tossed to Kuroda, who slapped a tag on Carp trying to score.
"The ball didn't go all the way to the backstop," Stewart said. "Fortunately it stayed somewhat close to where I could pounce on it pretty quickly."
New York added three runs in the seventh to close the book on Lackey, who allowed four runs and 10 hits in 6 1/3 innings. Cruz singled home Nunez for the second run, while Robinson Cano and Overbay rapped RBI singles off lefty Matt Thornton.
"He's so good," Lackey said of Cano. "He's one of those guys who almost has to get himself out. You try to make the odds go in your favor a little bit, but you just try to execute pitches and hope he hits it at somebody."
Cano's second RBI of the game, coming on a ninth-inning sac fly, gave Rivera a three-run lead to protect.
"That's what we have to do," Girardi said. "There's not too many nights when we're going to slug. That's not who we are. We have to pitch extremely well. We have to get distance from our starter and allow our bullpen to go to work and have a lead. Having a lead is really important."