WASHINGTON -- The New York Mets team plane arrived in the capital region Sunday night, hours after a second walk-off loss to the lowly Miami Marlins in three days in south Florida.

Mets manager Terry Collins was hoping his team could win two of three games against the Washington Nationals, who had pulled to within four games of the first-place Mets after trailing by 6 1/2 a few days earlier.

But New York did much more than that, sweeping the series with three pulsating comeback wins that stunned Washington fans and left the defending National League East champion Nationals closer to elimination after their bullpen failed them once again.

"It has definitely been fun. These guys are fun to watch," said Mets pitcher Jacob deGrom, after he picked up the win in a 5-3 victory over the Nationals on Wednesday night. "That was the goal when we came here: win all three. That is what we did."

Center fielder Yoenis Cespedes, who had two hits and is batting .312, smashed a two-run homer off former closer Drew Storen in the eighth to break a 2-2 tie after he had a three-run double in the win against Storen one night earlier.

It was the first time since Philadelphia in 2012 that the Mets came back to win three road games in a series.

Pinch-hitter Kelly Johnson led off the eighth with a pinch-hit homer off Stephen Strasburg to tie the game at 2-2. It was the second pinch-hit homer of his career.

"I am going to run some lefties up there and take a chance," Mets manager Terry Collins said of sending Johnson to hit for shortstop Wilmer Flores.

The Mets (78-61) now lead the National League East by seven games over the Nationals with 23 games left.

"I've dealt with a fair share of adversity in my career, so just to go dig down and get through," Storen said. "You've got to keep pushing. You've got to look forward. Like I said last night, you can't change the past, but you can control what's coming up."

Said Washington manager Matt Williams, who has been second-guessed all week on local sports radio for his handling of the bullpen: "Our bullpen is one of our strengths generally, and it hasn't been (recently). It's tough. I feel for those guys getting out there and giving up runs because they're not intending to, that's for sure."

Washington (71-68) lost six games in a row to the Mets after winning the season series 15-4 in 2014. The last time the Mets won the NL East title was 2006.

"It is fun to be on this team right now," deGrom said.

Washington center fielder Bryce Harper (.336 average) hit a solo homer in the eighth off former teammate Tyler Clippard to pull the Nationals to within 4-3. It was the second solo homer of the game for Harper, who had three hits and has 36 homers this year.

Mets left fielder Michael Conforto, who made a diving catch to end the eighth, had an RBI single in the ninth off closer Jonathan Papelbon to give the Mets some breathing room at 5-3.

Jeurys Familia pitched the ninth for the Mets and got his 39th save as he retired all three batters and got his third save in as many days.

"The biggest three games I had in my career," Collins said. "Huge comebacks and inspirational play by everybody. It was really, really great to be a part of."

Cespedes had lined a three-run double off Storen on Tuesday during a six-run seventh inning in an 8-7 win in which Washington had led 7-1.

Washington starter Strasburg (8-7) gave up three runs and struck out 13 before he was lifted with one out in the eighth. Strasburg struck out at least 10 batters for the 18th time in his career but had nothing to show for it.

Mets starter deGrom (13-7) gave up two runs on five hits with nine strikeouts in seven innings before he was lifted for a pinch-hitter in the top of the eighth.

Catcher Travis d'Arnaud had two hits for the Mets, including a solo homer. The Mets have scored at least three runs in 23 road games in a row.

Harper gave the Nationals a 1-0 lead in the first with a solo homer just over the fence in right against deGrom. It was the 35th homer of the year for Harper, who was hitless in his previous eight at-bats in the series.

The Mets tied the game at 1-1 in the second as d'Arnaud hit a solo homer to left off Strasburg. It was the 11th of the year for d'Arnaud.

The Nationals took a 2-1 lead in the fourth as Harper led off with a double and then scored on a one-out hit by Clint Robinson, the first baseman.

"I don't feel like we are out of any game," deGrom said. "These guys are fun to watch. Harper got me early. I threw the pitch where I wanted to. I wanted to keep us in that game."

NOTES: The Mets have now homered in nine games in a row to match a season high. ... Washington had three key players out of the starting lineup: 1B Ryan Zimmerman (left oblique), 3B Yunel Escobar (fever) and OF Michael A. Taylor (sore right knee). INF Danny Espinosa was in the starting lineup at second base with INF Anthony Rendon moving to third. INF Clint Robinson started at first and OF Matt den Dekker was in left field. ... The Nationals have an off-day Thursday and then will begin a series in Miami on Friday. Nationals LHP Gio Gonzalez (10-7, 3.96), will face Marlins RHP Jarred Cosart (1-4, 5.04). ... Mets RHP Bartolo Colon (13-11, 4.18), the reigning National League Pitcher of the Week, will pitch on Thursday in Atlanta against Braves RHP Shelby Miller (5-13, 2.81).