NEW YORK -- Four days before hitting one of his more significant home runs of the season, a walk-off blast to secure a 5-4 win for the Mets over the Nationals in the second game of a doubleheader on Thursday, Pete Alonso implored Mets fans to “believe in us” and to “smile” and to “know” that the team would turn things sharply in another direction.

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The Mets had lost nine of 11 at that point, appearing as lifeless as at any juncture of this 2021 season. As a result, the general public met Alonso’s words with a mix of skepticism and, in some cases, even scorn. Smiling was difficult when the Mets had given their fans little reason to do so. Believing seemed more difficult still.

Then Alonso went out and arced his homer just over the left-field fence at Citi Field to secure a three-game series sweep.

“I think this team has showed over and over again this season the fight that they have,” said outfielder Brandon Nimmo, who drove in all four of the Mets’ runs in their 4-1 win in the first game of the doubleheader. “So happy for Pete to come through in that last game. That’s huge. This series was huge. From here on out, every game is going to be big.”

Nimmo’s reference was mostly to a stretch of 13 consecutive games against the Dodgers and Giants beginning Friday. The looming presence of the two behemoths of the National League West made the matchup this week against the fourth-place Nationals that much more important.

In a series that rain disrupted multiple times, the Mets never quite did enough to make things easy. But after coming from behind to win a one-run game on Wednesday, they managed to secure two more victories Thursday.

The last of those ended only after Jonathan Villar hit a two-run homer in the sixth inning, Michael Conforto completed his second straight multihit effort and Trevor Williams gave the Mets an adequate spot start. Life was good until Trevor May and Jeurys Familia subsequently combined to allow three runs in the top of the seventh, casting gloom over Citi Field just as a collection of thunderclouds floated near the ballpark.

As ominous as both situations seemed, however, the storm -- both literal and figurative -- never came. Familia eventually wriggled out of the jam to keep things tied, before Alonso crushed a 2-0 fastball from Kyle Finnegan over the fence for the Mets’ ninth walk-off win of the season.

“Over the course of 162 games, this team is built to last,” Alonso said. “I feel that, and I know I’m not the only guy that feels that.”

As recently as two weeks ago, with the Mets maintaining their hold on first place in the NL East despite their injuries and struggles, belief in them was easier to find around the five boroughs. That changed quickly: When the Mets returned home following a miserable road trip through Miami and Philadelphia, even general manager Zack Scott offered bluntness in his assessment that the Mets had “played very mediocre baseball for most of the year” and “unacceptably bad” ball in recent days.

Scott’s charge was for his club to improve, and fast, with three games against the fading Nationals on the horizon. To appease him, the Mets swept a team that had not only traded away Max Scherzer, Trea Turner, Kyle Schwarber and others last month before the Trade Deadline, but also lost almost every game since.

Consider it a necessary step for Scott’s team, with more significant tests on the immediate horizon. Beginning Friday, the Mets will enter what Alonso called a “show-me stretch” of 13 straight games against the Dodgers and Giants -- the former a preseason World Series favorite that recently acquired Scherzer and Turner from the Nats, the latter a surprise team that’s owned MLB’s best record for much of the year.

If the Mets thrive over the next fortnight, or even just hold their own, it will mean more for their future prospects than a sweep over the dismantled Nationals ever could.

If they stumble, it could mean the end of their realistic postseason pursuit.

“If you want to be a playoff team, then you have to beat some other playoff teams,” Nimmo said. “These two teams are very, very good. They obviously have very good records and very good track records of success. So these next few series will be good tests of playoff baseball. I think that’s the significance of it, is just getting down to the nitty-gritty of the season and where we want to be.”