Within the past month, the Yankees managed to win 13 straight games but also endure losing streaks of four and seven games. The Mets began August in first place and ended it in third place, out of the playoff picture and apologetic that some of their stars had been flashing thumbs-down gestures to their own fans.

The streaky, star-crossed seasons of both teams converged this weekend in the first Subway Series played on the anniversary of the Sept. 11 attacks. The game began with a heartfelt ceremony honoring the victims on Saturday’s 20th anniversary, during which players from both teams stood intermixed on the foul lines for the national anthem, wearing hats honoring first-responder agencies such as the New York Fire Department and the New York Police Department. The teams then waged a nearly four-hour, back-and-forth contest in which the Yankees prevailed, 8-7, to halt a winless week.

The roller coaster of a game was fitting for how the seasons for both teams have gone.

“I think every day is the start of a streak,” Yankees Manager Aaron Boone said. “I believe in this team. I believe in this group. It hasn’t been pretty. It’s been ugly at times. But I don’t think this group will ever lose confidence in what we’re capable of when we’re at our best.”

While the Mets’ postseason chances have dwindled to only 4.3 percent, according to FanGraphs, the Yankees, who are fighting for an American League wild-card spot, needed Saturday’s victory just to tread water, as their primary competitors also had comeback wins.

But for New York’s teams, Saturday had emotions that went above and beyond the season. A sellout crowd with bipartisan sympathies repeatedly voiced call-and-answer chants of “Let’s go Mets” and “Let’s go Yankees,” with everyone joining in choruses of “U-S-A, U-S-A!”

“This was for the city,” said Yankees outfielder Aaron Judge, who homered twice and made a diving catch in the ninth inning.

“This was for the Yankees fans. This was for everybody affected on this day,” he said. “This was more than just a baseball game tonight. It was an honor to be able to be out there and be on that field and be able to represent New York. It’s tough to describe. I grew up in California, but my heart and my soul are in New York.”

Summoning that winning spirit has come in fits and starts for the Yankees. A loss to Toronto on Thursday night had capped what Boone called a “horrible homestand” that culminated with four defeats to the hard-charging Blue Jays. On Friday, with the skid reaching seven games in a loss to the Mets — the Yankees’ worst streak in 25 years — infielder DJ LeMahieu admitted that the Yankees were “beyond frustrated,” deeming his club “the streakiest team in the league.”

But on Saturday, the team that had dominated the majors not so long ago showed up.

The Yankees slugged three home runs in the second inning off Mets starter Taijuan Walker, and Judge hit his second of the night in the eighth to tie the game. And their brute strength was complemented by a little hustle with their winning run — the only one of eight not plated on a long ball — coming around thanks to a hard slide and an errant throw. Pinch-hitter Luke Voit grounded into what seemed destined to be an inning-ending double play, but Mets second baseman Javier Baez sailed his pivot throw wide of first base, allowing pinch-runner Andrew Velazquez to scamper home.

“You can still go in hard and make it a challenge, and he absolutely impacted that play and made a difference,” Boone said. “It was good to see a baserunning play, a hustle play, really pay dividends for us there.”

The Yankees’ rally ended what had looked like a storybook victory for the ages for the Mets, thanks to a go-ahead home run with an unmistakable echo. Just as the Hall of Famer Mike Piazza had belted a late-inning, two-run moonshot on Sept. 21, 2001 to help the Mets win the first major sporting event in New York City after the Sept. 11 attacks, so too did the franchise’s new starting catcher, James McCann, slug a two-run homer to take a late lead on Saturday. McCann had also tripled and scored in the bottom half of the second.

“Guys showed the resiliency once again, battling, and we showed that the whole year with guys not giving up despite that beginning they had against Walker,” Mets Manager Luis Rojas said.

The Mets, however, couldn’t sustain the lead, with reliever Trevor May allowing three runs as his team squandered a 7-5 lead. The loss left the Mets four games out of the second wild-card spot. This was their eighth loss this season when leading after seven innings.

While Saturday’s win helped the Yankees avoid falling behind Toronto in their own wild-card race — the Blue Jays won both games of a doubleheader against the Baltimore Orioles on Saturday to pull into a virtual tie for the second wild-card spot — there are still plenty of issues to hammer out.

More than three hours before Saturday’s first pitch, the Yankees were taking infield practice, a necessary slog after having looked remarkably sloppy in a lopsided 10-3 loss to the Mets on Friday. In the first inning, Yankees catcher Gary Sanchez had received a relay throw with the Mets’ Jonathan Villar still some 20 feet away from home plate. Yet Sanchez made only a tentative, high tag attempt on Villar, who never slowed and then slid in safely. Speaking of Friday’s game as a whole, Boone tagged it “just a poor performance, period.”

Several players spoke in a team meeting, full of reminders of the team’s potential. “We’re the same team that just won 13 in a row a couple weeks ago,” said outfielder Brett Gardner, who homered and singled on Saturday night.

Already contending with injuries to three-fifths of their rotation — Gerrit Cole, Jameson Taillon and Domingo German are all out — the Yankees have compounded their recent challenges by failing to get depth from their patchwork set of starters. Corey Kluber exited after four innings of four-run ball on Saturday, the sixth time in the last eight games in which the team’s starting pitcher failed to complete the fifth inning.

Saturday was the first of those contests they’ve won, but the stretch has left the Yankees wondering how to sustain this pace for the final 20 games of the season. After the win, Boone admitted he didn’t yet know who would start Sunday night. He had used all but two position players on Saturday as well.

“One of those where we needed everyone, and we used almost everyone,” he said.