Masahiro Tanaka outpitched David Price in their first matchup to win his fourth straight decision, and the New York Yankees ended Boston’s six-game winning streak Sunday night with a 3-1 victory over the Red Sox.

Starlin Castro keyed New York’s three-run fourth inning with an RBI double that scored Didi Gregorius from first base. No. 9 batter Austin Romine and Jacoby Ellsbury each added a run-scoring single with two outs off Price, who gave up 11 hits in 5 2/3 innings as the Yankees prevented a three-game sweep.

Following his team’s loss on Saturday, manager Joe Girardi said the Yankees needed to turn things around immediately and called Sunday night “probably as important (a) game that we’ve had in July in a long time.”

New York (45-46) responded with excellent pitching and a handful of timely hits.

Price (9-7) had only one strikeout following three consecutive outings with 10. Dustin Pedroia homered early for Boston, which remained two games behind first-place Baltimore in the AL East.

Tanaka (7-2) fanned seven with one walk over six innings of three-hit ball in his latest stingy performance on extra rest. Pitching with six days between starts, the Japanese right-hander improved to 6-0 in 11 starts with more than four days off.

He is 1-2 with a 5.33 ERA in his other eight games.

Tanaka had Red Sox hitters in baseball’s highest-scoring lineup chasing sliders and splitters below the strike zone. He threw just 87 pitches — but that was all the Yankees needed because their three big bullpen arms were all fresh and ready to go.

Dellin Betances, Andrew Miller and Aroldis Chapman combined for three hitless innings. Chapman worked the ninth for his 18th save in 19 chances, and the Yankees upped their record to 17-1 when all three pitch in the same game.

New York’s bullpen has thrown 19 straight shutout innings.

Boston hasn’t swept a series at Yankee Stadium since June 2011, and the Red Sox haven’t won seven in a row overall since June 1, 2014.

Price, who leads the AL with 141 strikeouts, fell to 14-9 in 34 career games (33 starts) against the Yankees.

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