Boston’s Bobby Dalbec, left, Rafael Devers, center, and Christian Vazquez celebrate a 10-2 win Sunday at Fenway Park. The victory prevented the Yankees from completing a sweep of all 10 games against the Red Sox this season. Steven Senne/Associated Press

BOSTON — Despite dismal results against the New York Yankees this season, at least the Boston Red Sox didn’t have to watch their longtime rivals enjoy clinching a playoff berth at Fenway Park.

They made sure of that by finally beating the Yankees this year.

Tanner Houck took a no-hitter into the sixth inning of his second major league start and Michael Chavis had a huge day at the plate as the Red Sox halted two long streaks with a 10-2 victory Sunday.

Boston ended New York’s 10-game winning streak and snapped a 12-game skid against the Yankees.

“A great experience. It’s a great rivalry that I remember watching growing up. Being a part of it was amazing,” Houck said. “Going deep into the game like that with a no-hitter is truly an unbelievable experience.”

Chavis hit two homers over the Green Monster and drove in five runs. Jackie Bradley Jr. went 4 for 5, and J.D. Martinez and Bobby Dalbec each had a solo shot.

It was Boston’s first win over the Yankees in 10 meetings this season. New York had matched its longest winning streak against the Red Sox, also winning 12 in a row in 1936 and from 1952-53 when Red Sox Hall of Famer Ted Williams was flying combat missions in the Korean War.

The loss temporarily kept the Yankees from locking up a playoff spot, but San Diego’s 7-4 win over Seattle later Sunday means the Yankees will go to the postseason for the fourth straight year.

Luke Voit hit his major league-leading 21st homer for the Yankees, who outscored their opponents 85-25 during the winning streak.

In a matchup of right-handed prospects on a breezy afternoon, the 24-year-old Houck mixed a sharp slider, sinker and a fastball in the low-to-mid 90s to keep the Yankees off balance until Tyler Wade lined a double into the right-center gap.

“Seeing that against a really hot offense like these guys have had, it’s great to see that stuff,” Boston Manager Ron Roenicke said.

Houck (2-0) gave up just that one hit and an unearned run. He struck out four and walked three in six innings.

“He’s got good stuff,” Yankees Manager Aaron Boone said. “I thought maybe we expanded a little bit on some pitches off the plate. He did a good job of working his two-seamer in, and then even changeup off of that. But he was tough.”

In his big league debut at Miami on Tuesday, Houck held the Marlins to two hits over five scoreless innings, striking out seven.

Deivi García (2-2) was roughed up for six runs and eight hits over three innings in his fifth career start. He felt his command was off.

“I battled with that today,” he said through a translator. “It kept me from being as aggressive as I wanted to be.”

With the Red Sox leading 3-0 in the third, Chavis hit a hanging slider that landed in the first row of seats above the Green Monster in left field for a three-run homer.

Chavis’ first homer came on a belt-high slider in the second inning and left Fenway completely.

“Just a bump here for him, but all things he can correct, and go out and do what we’ve seen in his next one,” Boone said about García.

DELAY

There was about a 10-minute delay with the Yankees batting in the eighth when someone started screaming from a camera stand above the center-field bleachers. The person threw something onto the field. The umpires gathered at home plate until the person was removed.

SPECIAL PLACE

García took the mound where his boyhood idol and fellow countryman, Pedro Martínez, spent much of his Hall of Famer career. The 21-year-old righty from the Dominican Republic even has number 45 – the number Martínez wore – written on the front of his belt.

TRAINER’S ROOM

Yankees: Outfielder Aaron Judge was not in the lineup. A strained calf limited him to one game between Aug. 11 and his return Wednesday. He played the first two games of the series, going 1 for 9 with two runs, three strikeouts and two walks. … Catcher Gary Sánchez was shaken up by a foul ball that ricocheted off his left arm and then neck, but he stayed in.

Red Sox: Roenicke gave shortstop Xander Bogaerts the day off and said outfielder Alex Verdugo (left hamstring soreness) and second baseman Christian Arroyo (back spasms) were unavailable.

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