WASHINGTON -- Heading into this weekend’s five-game series against the Nationals, a popular discussion topic around Nationals Park was how many the Mets would need to win to maintain their growing relevance in the NL East race. A common answer was four at minimum, with a five-game series sweep seeming like a possible bonus.

It would have done the Mets irreparable harm, then, to lose a Friday night opener in which they led for nearly the entire game. Rather than suffer that fate after Edwin Díaz blew his first save in six-plus weeks, the Mets rallied to a 6-2 victory in 10 innings to keep their postseason dreams alive. They’ve now won five in a row -- six, counting this week’s suspended game against the Marlins that technically went on their ledger for April.

Combined with the Braves’ loss to the Rockies about an hour later, the win moved the Mets within four games of the NL East lead for the first time since Aug. 16.

“As you can imagine, it’s great,” first baseman Pete Alonso said of the postgame clubhouse mood. “It’s awesome to rip off six in a row, especially against teams in the division. We’re just really happy with how we’ve performed, and we’re really looking forward to the rest of the season.”

It was Alonso who contributed the most important hit for the Mets, singling home Francisco Lindor in the 10th to give the Mets another chance to close out the win. After Díaz cracked for two runs in the ninth, including a Juan Soto homer, the Mets used Alonso’s hit as the fuel for a four-run rally. Kevin Pillar doubled home two more off Nationals reliever Austin Voth, before Jonathan Villar added an RBI single for his fourth hit of the night.

“I feel like we’re playing good, clean baseball, and the wins show that,” Alonso said. “I’m really excited for this last month.”

Friday wasn’t the breezy type of win the Mets envisioned early in the evening, when Rich Hill completed six shutout innings, Michael Conforto hit a run-scoring single and Alonso added a rare RBI triple. But it was the type of victory the Mets enjoyed often during the first half of the season, relying on a strong bullpen and timely hitting to win a bevy of close games.

“The most important part of how we’ve been playing is just how together and how united we’ve been,” Villar said through an interpreter, “just to continue going out there and to continue battling so we can get the results that we want.”

The difference in recent results has been stark. Upon finishing a 13-game stretch against the Dodgers and Giants that saw them go 2-11 to drop 6 1/2 games in the standings in two weeks, the Mets found themselves staring at an equally appetizing 15-game stretch against the fourth-place Nationals and last-place Marlins. Their play versus those two teams has been uneven, resulting in several tight finishes. But the Mets have nonetheless managed to win all but one of them, turning what was an 8 1/2-game deficit on the morning of Aug. 28 into a four-game margin entering Saturday’s play.

Their mathematical odds to make the postseason, according to FanGraphs calculations, have risen as high as 91.4 percent this season and dropped as low as 1.5 percent.

The reality check is that an uphill climb still awaits the Mets, considering all the factors working against them -- that four-game deficit, a shrinking calendar, a tougher schedule beginning later this month and a much easier path for the first-place Braves. But if the Mets can continue beating up on the Nats and Marlins for the next six days, they will at least give themselves a chance.

“We just have to win every possible game that we can,” Alonso said. “Regardless of what the standings are right now, we can only control what we can control, and that’s the team that we’re facing that day. So we just have to keep winning as many games as possible.”