NEW YORK — CC Sabathia shut down the Boston Red Sox for the fourth time this season and the New York Yankees got homers from Gary Sanchez and Greg Bird on the way to a 6-2 victory Thursday night in the opener of a pivotal four-game series.

Bird drove in three runs and Sanchez had two RBI as the second-place Yankees shaved Boston’s lead in the AL East to 41/2 games. This weekend set in the Bronx marks the final meeting of the season between the longtime rivals – and perhaps New York’s last chance to make a serious run at its first division title in five years.

New York maintained a tenuous hold on the league’s top wild card.

Sabathia (11-5) has more than done his part vs. the Red Sox, winning all four outings against them this season while compiling a 1.04 ERA in 26 innings. The 37-year-old lefty, making his 250th start for the Yankees, permitted only one run and four hits in six innings despite walking five Boston batters for the second time this year – equaling a season high.

Using a sharp slider, Sabathia pitched out of a first-inning jam and struck out six overall. With timely help from his defense, he improved to 8-0 in 10 starts this year following a Yankees loss.

David Robertson worked two scoreless innings and Dellin Betances walked home a run in the ninth before retiring Mookie Betts and pinch-hitter Mitch Moreland with the bases loaded to end a game that lasted 3 hours, 44 minutes.

Sabathia has won five straight starts against Boston dating to last September.

At the plate, New York finally solved left-hander Eduardo Rodriguez (4-5), who entered 4-1 with a 2.31 ERA in eight career starts against the Yankees. Even better, he had a 1.38 ERA over 26 innings at Yankee Stadium, yielding only one run in his last 18 innings at the ballpark.

But the Yankees tied it 1-all on Sanchez’s 28th home run in the third and went ahead when second baseman Eduardo Nunez misplayed Sanchez’s popup into an RBI single with runners at the corners and one out in the fifth.

Chase Headley doubled to start the sixth and Bird hit a two-run shot for his second homer in two days. The first baseman came off the disabled list Saturday after missing most of the season with ankle and foot injuries.

Didi Gregorius added an RBI single later in the inning, and Bird had a run-scoring single in the seventh.

Rodriguez was charged with five runs and 10 hits in five-plus innings.

NOTES: United States Supreme Court Justice Sonia Sotomayor, born in the Bronx, was in the crowd of 43,309. Of course, she held court in The Judge’s Chambers, the rooting section out in right field for power-hitting Yankees rookie Aaron Judge. Justice Sotomayor wore a big smile and one of the black robes handed out to fans in the faux jury box. She high-fived fans on both sides of her when Sanchez homered. …2B Dustin Pedroia (left knee inflammation) is expected to come off the disabled list when rosters expand Friday. He will be monitored as he progresses to playing nine innings on consecutive days, Manager John Farrell said. … RHP Matt Barnes (lower back strain) also is on target to be reinstated from the DL on Friday. … CF Jackie Bradley Jr. (sprained left thumb) is likely to return from the DL when eligible on Saturday, Farrell said. … LHP David Price (left elbow inflammation) felt good following a 20-pitch bullpen session Wednesday and threw again from a shorter distance. He is scheduled to get back on the mound Friday, increase his number of pitches and hopefully mix in some change-ups. “An encouraging day today the way he came in and the way he felt,” Farrell said. … C Christian Vazquez was shaken up when Sanchez’s backswing knocked off his mask in the sixth. Vazquez was checked by Farrell and a trainer but remained in the game. … LHP Robbie Ross Jr. had back surgery Wednesday and is expected to be ready for next season, the team said. … DH Matt Holliday (back) could come off the DL this weekend, Yankees Manager Joe Girardi said. … OF Clint Frazier (strained left oblique) is “definitely getting closer” to a return from the disabled list, Girardi said. New York anticipates him trying to begin a minor league rehab assignment sometime next week.

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