NEW YORK -- Following another frustrating loss on Saturday, manager Joe Girardi didn't hesitate to place his label on the next game.

"This is probably as important (a) game that we've had in July in a long time tomorrow."

Those were Girardi's words as the Yankees faced the possibility of being swept by the Boston Red Sox and falling three games under .500.

On Sunday, Masahiro Tanaka delivered as significant a performance as possible, pitching six effective innings and combining with three relievers on a three-hitter as the Yankees salvaged the finale of a three-game series with a 3-1 victory over the Boston Red Sox.

"We didn't necessarily have a meeting and talk about how important tonight's game was but I think everybody understood how important we needed to win today," Tanaka said through a translator.

New York beat the Red Sox for the third time in nine meetings and scored all their runs in the fourth inning off David Price (9-7). Starlin Castro had an RBI double before Austin Romine and Jacoby Ellsbury added run-scoring singles.

The Yankees (45-46) moved to within one game of .500 for the 17th time since May 21 and are eight and a half games behind first-place Baltimore, which comes in for a four-game series Monday.

"A good one," Yankees right fielder Carlos Beltran said. "I think being able to take this one was a must-win for us today."

"It was (satisfying)," Girardi said. "I thought it was really important and we needed a big performance from Masahiro."

Tanaka made one mistake while continuing to pitch well on extended rest. Pitching on extended rest due to the All-Star break, Tanaka allowed a home run to Dustin Pedroia three minutes into the game and little else.

"He was just missing barrels all night," Pedroia said.

Tanaka allowed all but one of his baserunners within the opening two innings. He retired nine in a row before a double in the fifth by Brock Holt and 13 of the final 14 hitters he faced.

He turned things over to the bullpen after 87 pitches when his night ended with a warning track fly ball to David Ortiz.

"He was really good," Girardi said.

Dellin Betances pitched a perfect seventh, Andrew Miller fanned Pedroia for the final out of the eighth with a man on first and Aroldis Chapman secured his 18th save in 19 chances by getting Hanley Ramirez to bounce into a double play.

Ortiz was 0-for-3 with a walk and 2-for-11 in his penultimate series at Yankee Stadium before his retirement.

The Red Sox produced their second-fewest hit total and had a season-high six-game winning streak stopped.

Price was duplicate the success of his past three outings as he allowed three runs and 11 hits in 5 2/3 innings. Price allowed at least 11 hits for the ninth time in his career and it was the fourth instance against the Yankees.

"To be the guy that goes out there and doesn't help us win that seventh (in a row), that's tough," Price said.

Boston took a 1-0 lead three minutes into the game when Pedroia sent a 2-1 pitch over the left-field wall for his ninth home run of the season.

After Tanaka struck out the side in the fourth, the Yankees evened the score when Castro's double to left field brought home Didi Gregorius from first base.

New York went ahead two batters later when Castro scored on Romine's single up the middle off the top of Pedroia's glove.

The lead grew to 3-1 when Ellsbury blooped a single to center and Boston center fielder Jackie Bradley Jr. was charged with an error when his throw sailed over catcher Sandy Leon's head.

NOTES: New York 1B Mark Teixeira was not in the lineup after fouling a ball off his left foot on Saturday. After the game manager Joe Girardi said Teixeira was sore and would be out a "few days" ... Teixeira had a CT scan on his left foot, and about 30 minutes before Sunday's first pitch, the Yankees said the results were negative. Teixeira also had X-rays on Saturday, which were negative. ... Boston LHP Drew Pomeranz threw a 35-pitch bullpen session ahead of his Red Sox debut on Wednesday against San Francisco. Asked about being traded four times in his career, Pomeranz said, "I've done literally everything there is to do on a baseball field as a pitcher. I'm pretty prepared for anything. You could shove me out there in any situation, I've done it." ... Boston RHP Junichi Tazawa (right shoulder impingement) threw all of his pitches during a 40-pitch bullpen session. Red Sox manager John Farrell said Tazawa would likely throw a simulated game on Tuesday at Fenway Park.