Bryce Harper, right, and the Nationals picked up their second straight victory against the Mets. (Mike Stobe/Getty Images)

The challenge the Washington Nationals faced Tuesday, on what most involved agreed was the coldest evening of the year, was to revise history a day after making it. The comeback they staged Monday night seemed like the kind of thing that could start a turnaround, but momentum is fickle. For that rally to matter, the Nationals needed to play like a team transformed. For that big inning to become as pivotal as it felt, they needed to turn one good evening into two.

In a 5-2 victory over the New York Mets, the Nationals did just that, looking like an entirely different team than the one that could barely light a spark at times this season let alone tend a lasting flame. They scored early, and they added runs late. Gio Gonzalez started and left with a lead. The bullpen, overworked by days of close games, held on through fatigue.

The Nationals secured a series win and climbed back to .500 with a good, clean win — exactly the kind of game that has eluded them so far, exactly the kind of game their rookie manager, Dave Martinez, preached they should play all along.

“I truly like that we’re doing the little things,” Martinez said. “. . . That’s how you win games.”

Through the few ups and many downs of the early part of the season, the Nationals handed their opponents extra outs, both with recklessness on the bases and avoidable lapses on defense. After more than one close loss, Martinez expressed frustration with the habit, a message he conveyed to his coaches in the hopes that they would be able to make the tweaks necessary to tighten his team’s play. The rookie manager himself had long since made his position on mistakes like those clear.

“His number one rule from Day 1 was don’t give them more than 27 outs,” shortstop Trea Turner said. “I guess that’s more of a defensive mind-set, but it’s still playing the game clean. Then when we get more than 27 outs on offense, it makes it harder on them.”

Turner played a standout game defensively, seizing an out from the brink of a base hit with a diving play and throw across the diamond in the first. He had already set the tone for the evening with a leadoff double off the center field wall, an unofficial signal that the momentum the Nationals accumulated in the eighth inning Monday night had not evaporated in the interim.

Turner singled again to start a rally in the third, one that continued with a base hit from Howie Kendrick and a sacrifice fly from Bryce Harper. An inning later, Wilmer Difo flung his bat at a two-strike pitch from Mets starter Zack Wheeler to bloop a single that scored a run. Pedro Severino held his hands back on a curveball to knock an RBI single moments later. Ryan Zimmerman, who was 2 for 21 with runners in scoring position entering Tuesday night, chipped in a two-out single to score insurance in the seventh. Severino hit a chopper to drive in a run in the eighth. Given opportunities, the Nationals created runs and forced the Mets to earn their 27 outs.

“I looked up in the eighth inning, and we had three strikeouts or something,” Turner said. “That’s pretty hard to do with today’s pitchers.”

The Mets made things similarly tough on Gio Gonzalez, who did exactly what a starter should do on a night he is not dominating — bend but not break. The Mets fouled off pitches and forced Gonzalez’s pitch count high in the middle innings, but when he got into trouble he limited damage and left after 5⅓ innings in which he allowed two runs on eight hits and struck out five. Gonzalez is 11-1 at Citi Field, a phenomenon he couldn’t explain.

“The food?” he posited. “The airplanes?”

Whatever the reason, he left in position to win the game, but he left a two-on, one-out jam as he gave way to Sammy Solis, who had the difficult duty of keeping the tying run at third base. Solis got out of it.

An inning later, Ryan Madson got into a two-on, one-out jam in the seventh against the heart of the Mets’ order, but he struck out two batters to extricate himself. Brandon Kintzler gutted out a 27-pitch eighth in his third consecutive day of work, and though he will need a rest, he did not break.

“[This is] really big,” said Sean Doolittle, who earned his third save with a scoreless ninth. “I know it’s early. I know it’s the middle of April still, but for the stuff that we’ve already dealt with this season, coming off that homestand that we just had, to start off a long road trip like this is really, really good.”

For so long, the Nationals couldn’t get the key outs or key hits they needed. On Tuesday, a day after a rally that seemed to remind that things can go well sometimes — often, even — they secured key outs and mustered key hits. A day after they nearly fell seven games behind the Mets in the National League East, they climbed to within four, within one win of a much-needed series sweep. History will now say that eighth-inning rally mattered, because it lifted them out of their gloom. The question now is how much higher they will climb.