BOSTON - A contact pitcher for the visiting team making his Fenway Park debut wouldn't seem to be a good situation.

But it resulted in one of Nathan Eovaldi's best starts of the season.

The 25-year-old righthander kept the ball in play all afternoon (with one exception), helping the Yankees to a 4-2 victory over the Red Sox on Saturday in front of a sellout crowd of 36,611.

The victory was the 12th in 15 games for the Yankees (15-9), who guaranteed themselves a fifth straight series win after losing three straight series to start the season.

"That first week we didn't look too good," Joe Girardi said. "But we sure have turned it around."

Eovaldi (2-0) allowed two runs and seven hits, including Dustin Pedroia's solo homer, in 62/3 innings. He had allowed three runs and eight hits in 51/3 innings in a 6-5 loss to the Red Sox on April 10.

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Eovaldi, who lowered his ERA from 4.15 to 3.81, walked one and struck out two. His final line would have read a bit better had reliever Chris Martin not allowed Mookie Betts' double off the Green Monster with two outs in the seventh. That allowed an inherited runner to score and made it 3-2.

"I try not to let ballparks dictate how I throw," Eovaldi, a career National Leaguer until this year, said of his mind-set going into his first career start at Fenway Park, hardly known as a pitcher's park. "I feel like my stuff's good enough to where if I can locate, I should be able to get outs."

Brian McCann said Eovaldi's ability to pitch "in" allowed him to navigate through Boston's dangerous lineup with minimal damage.

"When he pitches in, they had to cheat to that, and once they started cheating, then he can start expanding," McCann said. "He pitched to both sides of the plate effectively and had them off-balance. When you pitch in at 96, 97 [mph], that's hard to hit."

Brett Gardner went 2-for-4 with three RBIs to raise his average to .319. He had an RBI double to leftfield in the third and a two-out, two-run single in the fifth off lefthander Wade Miley.

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Justin Wilson pitched a scoreless two-thirds of an inning in the eighth, getting David Ortiz to ground out, walking Hanley Ramirez and striking out Pablo Sandoval.

Dellin Betances pitched the final 11/3 innings, striking out all four batters he faced -- including Mike Napoli with a 98-mph fastball to end the eighth -- for his second career save and first this season.

Chris Young's sixth home run, a solo shot in the ninth off righthander Alex Ogando, gave Betances a 4-2 cushion.

"We're a fearless group down there," Betances said of the bullpen, which leads the majors in strikeouts (101 in 872/3 innings) and has a 1.64 ERA. "No matter who's out there, we believe they can get the job done."

Eovaldi has done just that, as the much-discussed transition from the National League to the American League has not been a factor. Eovaldi's best two starts of the season have come against the powerful lineups of the Tigers and Red Sox.

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"I just think it shows you the ability that he has," Girardi said.

Said Eovaldi: "I'm very confident in my abilities being able to pitch. Every pitcher's dream is to be able to pitch in the World Series, and you're going to be facing the best hitters at that time. So it's just small steps toward the bigger goal."