Tanaka (3-1) tossed a three-hitter to win a third consecutive start. It was the fifth complete game of his career and his first since 2015. He didn't walk anyone, and he struck out three in raising his career record to 42-17, 6-2 against the Red Sox.
Tanaka retired the last 14 batters, good for 15 outs, and needed 97 pitches to complete his second career shutout.
The Yankees, who started the season 1-4, are 12-3 since.
Sale, acquired by the Red Sox in a big offseason trade of major Boston prospects, continued to be the victim of non-support. He held the game close until the Yankees scored two in the ninth. He wound up charged with three runs (two earned) on eight hits with 10 strikeouts and no walks in eight-plus innings. It was his fourth straight double-digit strikeout game.
Sale fell to 1-2 with a 1.19 ERA.
Matt Holliday's sacrifice fly in the fourth inning was enough to beat Sale, who has received a total of four runs of offense while on the mound for his five Red Sox starts.
Sale allowed three straight singles to start the ninth, with Holliday bringing home a run. Starlin Castro greeted reliever Heath Hembree with an RBI single.
Hanley Ramirez had two singles and was the only Red Sox runner to reach second base as the slumping Boston bats continued to flounder. Boston (11-10) scored one run in the past two games and has scored 13 in the past seven. The Red Sox have been shut out in three of those seven games.
A passed ball by Sandy Leon helped the Yankees grab the lead in the fourth, with Holliday battling through a tough at-bat to produce his ninth RBI as a Yankee.
NOTES: SS Didi Gregorius, who sustained a right shoulder injury at the World Baseball Classic, will return to the Yankees' lineup Friday night after missing the first 20 games of the season, while C Gary Sanchez (biceps) begins a rehab in Triple-A on Monday. ... Boston claimed UT Chase d'Arnaud off waivers from the Atlanta Braves and moved RHP Carson Smith from the 10- to the 60-day disabled list after he experienced a setback in his rehab from Tommy John surgery. ... LHP CC Sabathia faces Baltimore in New York's opener of a home three-game series with the Orioles on Friday night, while LHP Drew Pomeranz goes for Boston to open a three-game home interleague series with the Chicago Cubs. ... The game time of 2 hours, 21 minutes was the shortest nine-inning contest in the rivalry since a May 6, 1994, game ran 2:13.