Is this four-game sweep of the Yankees the start of the run that saves the Red Sox’ season?

For weeks now, Red Sox players, interim manager Chad Tracy, and chief baseball officer Craig Breslow have acknowledged the team needs to go on a run to save its season. Otherwise, there would be little choice but to become sellers before the Aug. 3 trade deadline.

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Is this finally the start of that run?

In a game of ridiculous twists and turns decided by a series of unlikely heroes, the Sox scored three runs in the 10th inning to beat the Yankees, 5-4, and complete a four-game sweep of their rivals.

That’s seven wins in the last 10 games for the Red Sox. At 36-46, they’re somehow only 4½ games out of a wild-card berth in the American League.

Yes, they would have to pass six teams to get to the playoffs. But given the wretched state of the American League, it’s not impossible.

“That was something,” said Tracy, after watching five players go to the plate in the 10th and contribute to the rally in some way.

Indeed, it was. The Sox and Yankees have made a habit of playing unusually dramatic games over the years, but this was particularly nutty.

Sonny Gray no-hit the Yankees for 7⅓ innings and left the game with a 2-0 lead. He returned to the clubhouse and watched his victory disappear when Aroldis Chapman allowed two runs in the ninth.

One of the runs was unearned thanks to a throwing error by Gold Glove right fielder Wilyer Abreu.

It got worse. The Sox allowed two more runs in the 10th inning, with a second throwing error by Abreu accounting for two more unearned runs. Care to guess how many times he’s committed two errors in a game? That’s right, never.

The Red Sox, who have struggled to score all season, had the bottom of their order coming up in the bottom of the inning.

With Caleb Durbin the automatic runner at second, Anthony Seigler slapped an RBI single to right field to drive in a run. Masataka Yoshida then doubled to right field, sending pinch runner Andruw Monasterio to third.

Yoshida turned what looked like a single into a double by challenging the arm of Cody Bellinger and hustling to second base. That changed the tenor of the inning.

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“Bellinger, he’s a great fielder. But the way he caught it, I thought I had a chance,” Yoshida said.

Tsung-Che Chen, who joined the team Friday, delivered a sacrifice fly to score Monasterio. Jarren Duran, who has been one of the worst hitters in baseball this month, singled to center to win the game.

It was only his third RBI in 28 career at-bats as a pinch hitter.

“That was sick,” Gray said.

Duran looked more relieved than celebratory afterward.

“I’m sure people gave up on us. But nobody in this clubhouse gave up,” he said. “We’ve shown it this whole series. I feel like we fought hard this entire series, and it showed in the last game. I’m just really proud of this team.”

Tracy, who managed his first Yankees-Sox game at Fenway on Thursday, looked wiped out afterward.

“The vibe in the stadium when they’re here is just different,” he said. “It really is. So we feel really good about what we just did. But also know we have to keep it going.”

He’s right. It’s too soon to say sweeping the Yankees will propel the Sox into contention. Let’s see how they handle the Nationals, who arrive at Fenway for a three-game series starting Monday.

But it’s not without precedent. The 1996 Red Sox were 34-48 after 82 games and finished the season with 85 wins. They didn’t make the playoffs, but it was an interesting summer.

Those Sox had Roger Clemens — who was at the ballpark on Sunday calling the game for NBC — and got a monster season from Mo Vaughn, who had 44 homers and drove in 143 runs.

This team needs to improve offensively, but the Sox managed to score 21 runs in four days against the Yankees.

“We’ll celebrate this one. We’ll celebrate the weekend, and then we’ll come in [Monday] and continue to move forward,” Gray said. “I know I will and think everyone else will as well.”

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