WASHINGTON — The Mets were in the midst of a sloppy game and a sloppy stretch of games.

They had failed defensively, they had failed repeatedly in big spots with their bats and in one instance they appeared to fail mentally.

All was forgiven, though, when Francisco Lindor and Drew Smith did not fail.

Lindor knocked a bases-clearing single in the sixth inning Friday night that drove in all the runs the Mets needed, and Smith picked up his first career save in a 3-2 win at Nationals Park to open a four-game series.

The otherwise-struggling Mets (19-20) won for just the third time in their past 10 games.

The majority of those games have come against subpar competition, including the Nationals (16-22).

The Mets scored in just one inning — and on just one swing — after plating two runs in their past two games.

Their hitting frustration is not over, but perhaps Lindor’s moment can serve as a turning point.

“Every game, to me, from now on I guess it means more,” said Lindor, who drilled the third three-run single in franchise history, matching Tug McGraw (1970) and Edgardo Alfonzo (1997). “We haven’t been playing to the level we want to play.”

The Mets were down, 2-0, in the sixth inning in large part because of a lack of clutch hits and an error by Lindor.

As Lindor stepped up with the bases loaded in the sixth, the Mets were 0-for-5 with runners in scoring position on the night and on track for another frustrating defeat.

But Lindor turned on a two-out, full-count, inside fastball from Carl Edwards Jr. and served it into the gap in right-center field.

Brandon Nimmo, running from first base on the pitch, surprised the Nationals and went all the way around, drawing a too-late throw from CJ Abrams that enabled Lindor to take second.

“I’ll just trust Joey [Cora] and whatever he sees,” Nimmo said of the aggressive third-base coach.

It was the only hit the Mets collected with runners in scoring position and the only they needed because of clutch pitching.

Tylor Megill, who is fighting to stay in a rotation that is expected to welcome back Max Scherzer and Carlos Carrasco within the next week, battled for five innings in which he allowed two runs (one earned) on four hits and four walks.

He left with the lead, and excellent bullpen work from Jeff Brigham, Adam Ottavino, David Robertson and Smith no-hit the Nationals over the final four innings.

Robertson was stretched to 1 ²/₃ innings and walked two in the ninth, putting the potential winning run on first base.

Manager Buck Showalter summoned Smith, who struck out Lane Thomas for the first save of his five-year career.

“That’s kind of what you dream of as a kid, coming in,” said Smith, before correcting himself. “Obviously, maybe a clean inning is what I really dream of.”

Prior to Lindor’s sixth-inning swing, the game had been defined by Mets misplays, physical and otherwise.

They should have scored a run before Lindor even stepped up.

With Mark Canha on second and Starling Marte on third without an out, Brett Baty hit a soft roller that pitcher Andres Machado fielded.

Marte, going on contact, was thrown out at the plate, while Canha, not running on contact, remained at second.

The next batter, Francisco Alvarez, grounded out to the right side, which would have scored Canha had he advanced to third previously.

But after Nimmo walked, Lindor ensured the mental error didn’t matter — and ensured his own physical error didn’t matter.

In the bottom of the fourth, with Alex Call on third and one out, Jake Alu grounded a ball to Lindor, who appeared to want to throw home — but took his eye off the ball, which glanced off his glove and into the outfield.

That allowed Call to score and Alu to end up on second.

Such was the Mets’ luck through the early innings.

They had mounted significant threats in the first three innings only to strand seven runners on base.

They finished 1-for-9 with runners in scoring position, but the one loomed large.

“Winning today doesn’t mean that everything’s fixed and that we’re going to go on an absolute tear,” Nimmo said. “But it also doesn’t mean that.”