BOSTON -- Xander Bogaerts and Kyle Schwarber homered off Yankees ace Gerrit Cole, and Nathan Eovaldi took a shutout into the sixth inning to help the Boston Red Sox beat New York 6-2 Tuesday night in the AL Wild Card Game.

Bogaerts also made a perfect relay to throw out Aaron Judge at the plate when the game was still close, sending the Red Sox into the AL Division Series against the Tampa Bay Rays. Game 1 in the best-of-five matchup is Thursday night in St. Petersburg, Florida.

With Bucky Dent in the crowd and Aaron Boone in the Yankees dugout, Boston chased Cole in the third inning and beat New York in the playoffs for the third straight time. The Yankees, who lead the majors with 27 World Series championships, have not won it all since 2009.

A year after baseball took its postseason into neutral site bubbles to protect against the pandemic, a sellout crowd of 38,324 -- the biggest of the year -- filled Fenway Park to rekindle one of the sport's most passionate rivalries. Enough Yankee fans were among them to fuel a raucous back-and-forth of insulting chants.

It was the fifth playoff matchup between the longtime foes, with Boston taking a 3-2 edge. That doesn't count the 1978 AL East tiebreaker -- technically regular season Game No. 163 -- that the Yankees won thanks to Dent's homer into the net above the Green Monster.

Boone, the former infielder who is now the Yankees manager, added to the heartbreak with his 11th-inning walk-off homer in Game 7 of the 2003 AL Championship Series.

The Red Sox haven't lost to them since.

They got their revenge the next year when they rallied after losing the first three games of the ALCS to eliminate the Yankees, then went on to win their first World Series title in 86 years. They won three more Series, in '07, '13 and in '18 when they knocked out the Yankees in the divisional round.

Any lingering pain disappeared into the centerfield bleachers in the first inning on Tuesday night.

Unlike Dent, who barely cleared the left-field wall that sits just 310 feet from home plate, Bogaerts drilled a line drive 427 feet to straightaway center. And unlike Carlton Fisk, who contorted his body to will the ball fair in Game 6 of the 1975 World Series, Bogaerts interrupted his home run trot only to flex for the Red Sox dugout.

Cole was pulled after he allowed Schwarber's third-inning solo shot and put two more men on with nobody out. In all, he was charged with three runs on four hits and two walks, striking out three in two-plus innings.

Eovaldi only allowed two hits through five innings before giving up a solo home run to Anthony Rizzo -- Schwarber's teammate on the 2016 Cubs championship team -- that sparked the first excited cheers from the Yankees fans in the crowd.

After an infield single by Judge, Ryan Brasier relieved Eovaldi and gave up a wall single to Giancarlo Stanton. Mistakenly waved home by third base coach Phil Nevin, Judge was easily thrown out at the plate -- 8-6-2 -- by the team that led the majors with 43 outfield assists during the season. (The Yankees made 22 outs at home this season, tied for the most in baseball.)

In all, Eovaldi allowed one run on four hits in 5 1/3 innings, striking out eight. Alex Verdugo doubled in one run in the sixth to make it 4-1 and then singled in two more in the seventh to give Boston a 6-1 lead.

Stanton, who singled high off the wall early, hit a solo homer in the ninth.

The teams swapped places twice in the last 10 days of the season, starting with the Yankees' three-game sweep in Boston Sept. 24-26 that moved them into the first wild-card spot. At one point, Major League Baseball ran through the tiebreaker scenarios, and the Yankees had to choose whether they would want to play in Boston or Toronto to break a four-way tie.

They chose Boston.

Although the tiebreakers weren't necessary when both teams finished ahead of Toronto and Seattle -- with identical 92-70 records, Boston earned home-field by virtue of a 10-9 head-to-head record -- word of the Yankees' decision inevitably made it to the Red Sox clubhouse.

"We knew about it. We don't really talk about it because we had some business to take care of ourselves," Red Sox center fielder Kiké Hernandez said before the game. "They wanted us and they got us now, so win or go home. That's it."