The Yankees chased Aaron Judge into the outfield early Sunday night, swarming him in a bouncy, gleeful embrace. Now they will follow Judge to the playoffs.

Judge is the Yankees’ cornerstone, the slugger who has led them for half a decade as they’ve tried to return to the World Series. This season was more trying than most, with alternating lengthy stretches of captivating and confounding play. But Judge assured it would continue by topping a tense day at Yankee Stadium with a game-winning single in the bottom of the ninth inning to beat the Tampa Bay Rays, 1-0.

“It’s been a crazy, wild, tough year,” Manager Aaron Boone said. “Fitting that it would come down to the last day to get in. But I love our group, I love our guys, I love our compete. It hasn’t always been pretty, but we’re ready to take our shot. We know we can beat anyone when we’re at our best.”

The Yankees’ first test will be the rival Boston Red Sox, who earned a 7-5, comeback road victory over the Washington Nationals with four hits and two homers from Rafael Devers. The Yankees and Boston finished the regular season with identical records (92-70), but the Red Sox will host the American League wild-card game on Tuesday at Fenway Park because they took the season series from the Yankees, 10-9.

The Yankees will start their ace, Gerrit Cole, with the Red Sox lined up to start the former Yankee Nathan Eovaldi.

“You can feel that Yankees-Red Sox is a little different,” said starter Jameson Taillon, a first-year Yankee who collected the first 10 outs on Sunday. “I’ve never experienced anything like it. Red Sox-Yankees, even in the regular season, back in June, felt different, so I’m sure it will be a crazy game. No one I’d rather have on the mound than Gerrit Cole.”

Judge, a three-time All-Star, set up the date with his first career game-ending hit. He connected on a hard shot up the middle that deflected off the glove of Rays pitcher Andrew Kittredge. Second baseman Brandon Lowe picked the ball up and fired an off-balance throw to the plate, but the pinch-runner Tyler Wade slid head-first, ahead of the throw, to touch off the celebration.

“It took us a while to get going,” Judge said. “But we got a spot in the playoffs. All you’ve got to do is just get in.”

It was the first Yankees game in more than three years to be scoreless into the ninth inning, and the Yankees managed only one hit through the first eight. They are missing a star infielder after putting D.J. LeMahieu on the injured list before the game with a sports hernia, but Rougned Odor — the third baseman batting .201 at game time — came through to start the winning rally.

Odor led off with a single off the left-hander Josh Fleming, and Wade ran for him. After an out, Anthony Rizzo lashed a single to right, advancing to second on a throw home with Wade holding at third. Then Kittredge, a right-hander, came in to face Judge, who delivered the Yankees to their 57th postseason appearance and fifth in a row.

“We know our ultimate goal is not just to get in,” Judge said, after partying with teammates in the clubhouse. “It was a good celebration, but now it’s time to get to work. All that other stuff, the 162, that was spring training. Now it’s time to get to the regular season and get it rolling.”

The Yankees used a six-man pitching relay to subdue the Rays, and one out stood above the rest. With two out in the sixth inning, shortstop Gio Urshela charged toward the third base dugout for a sinking foul pop from Austin Meadows. Urshela snagged the ball and hurtled headfirst across the steps of the Rays’ dugout, through an opening in the railing.

“He looked like a missile flying in there,” Boone said. “It scared me to death.”

Urshela, who was playing in a shift, limped away on his own and stayed in the game until the ninth inning. He said he initially thought he might have been seriously injured, but was relieved to have not hit his head. He felt soreness in his legs and elbow but said he could play on Tuesday.

“I felt a lot of pain in that moment; I didn’t even know what was happening,” Urshela said. “But thank God I feel really good. It could be worse.”

Urshela’s effort was a highlight of an inspired all-around performance by the Yankees, who had lost the first two games of this series, risking the need for a play-in game just to get to the wild card.

The Yankees rarely take so long to secure a trip to the postseason. This was only the fifth time they had entered the final day of the regular season with a chance to clinch a playoff spot — and one of those regular seasons, 1978, ended with a clash at Fenway made famous by Bucky Dent’s surprise three-run homer over the Green Monster.

That game — a playoff, but technically part of the regular season — propelled the Yankees to the American League Championship Series. At stake Tuesday will be a trip to Tampa Bay for the division series, and the Yankees and the Red Sox made sure that it would take only one game.

The day began with the Toronto Blue Jays and the Seattle Mariners also alive for a wild-card spot, setting up the possibility of a three- or four-way tie for two spots. But the Yankees and the Red Sox both led Toronto and Seattle by a game, and when they won, the Blue Jays and the Mariners were eliminated.

(For the record: Toronto beat the Baltimore Orioles, 12-4, but the Mariners lost to the Los Angeles Angels, 7-3, as Shohei Ohtani connected for his 46th homer and 100th run batted in.)

In the National League, the five-team playoff field was decided before the weekend, but the Los Angeles Dodgers had a costly few days. They could not wrest the West division title away from the San Francisco Giants, and lost two major contributors to injury.

Clayton Kershaw, the best left-handed starter of his generation, left Friday’s game with a recurrence of pain in his elbow and forearm; he said he was likely done for the season. Max Muncy, the Dodgers’ leader in homers and runs batted in, left Sunday’s game after a play at first base in which a runner collided with his outstretched wrist as he reached for the ball. Manager Dave Roberts told reporters later that Muncy was unlikely to play in the wild-card game against the St. Louis Cardinals or a possible division series.

The Dodgers’ streak of winning eight division titles in a row ended despite their blistering finish to the season. They went 44-13 after acquiring Max Scherzer and Trea Turner in a trade with Washington on July 31, and finished with 106 victories to tie a franchise record.

But the Giants never slumped, and the Dodgers will host St. Louis in the N.L. wild-card game on Wednesday.