WASHINGTON - The ball had barely come off the bat of Yoenis Cespedes. But in the Mets' bullpen, just beyond the leftfield fence, they knew.

The impact must have sounded like the starter's gun at a track meet, for as soon as the drive cut through the air on a muggy night for a wake, the Mets' relievers sprang to their feet.

They whooped and hollered and waved towels, tracking the path of Cespedes' blast, all the way over the fence. They jumped up and down here in the silence of Nationals Park, rejoicing in the defining moment of a 5-3 victory, one that capped a three-game sweep and squeezed the life out of the Nationals' season.

"You feel pretty good about taking the air out of the stadium," said Kelly Johnson, whose game-tying, pinch-hit homer in the eighth paved the way for Cespedes' go-ahead two-run blast off Drew Storen later in the inning.

In all three games the Nationals led. In all three games the Mets rallied to win. In the process, they departed the nation's capital in possession of a commanding seven-game lead in the standings with only 23 to play.

"This has been the biggest three games I've had in my career," said Terry Collins, who is inching closer toward his first postseason berth in 11 years as a manager.

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Perhaps just as critically, the Mets left their main rivals in tatters, victimized by three straight bullpen meltdowns, their stomach for playoff-caliber baseball once again called into question.

Not even sheer brilliance by the Nationals' two brightest stars, Bryce Harper and Stephen Strasburg, could spare them from buckling against the Mets.

Harper bashed a pair of homers and a double, snapping a season-long skid against the Mets. Strasburg looked unhittable, striking out 13 Mets over 71/3 innings of dominance.

While Mets righthander Jacob deGrom (13-7, 2.40) held the Nationals to two runs over seven innings while racking up nine strikeouts, Strasburg nearly rendered him an afterthought.

Of Strasburg's 13 strikeouts, nine came on his curveball. At one point, he retired 12 in a row. He went four innings between allowing hits

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Still, the Mets simply pecked away at Strasburg, almost as if to wait him out.

With the Mets trailing 2-1 in the eighth, Collins lifted Wilmer Flores for Johnson, who pulled one of Strasburg's offerings into the rightfield stands. It was just his second career pinch-hit homer, and the beginning of the Nationals' unraveling.

Later, when embattled Nationals manager Matt Williams emerged from the dugout to retrieve the righthander after Curtis Granderson's single, the fans unleashed a torrent of boos, anticipating that what would follow might sting.

They were right, of course. Storen made the grave mistake of leaving a belt-high slider for Cespedes, who has carried the Mets since his first game shortly after the July 31 trade deadline.

It was the knockout blow.

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"I don't know how it works, but he should be in the discussion for the NL MVP," Mets captain David Wright said of Cespedes, who is hitting .308 with 14 homers and 36 RBIs since coming from the Tigers.

Harper answered with a homer in the eighth off Tyler Clippard, his second of the night, but the Mets got the run back in the ninth on an RBI single by Michael Conforto.

Closer Jeurys Familia nailed down his 39th save with a 1-2-3 ninth. By then, fans had already trickled out of Nationals Park, a "Let's Go Mets!" chant filling the silence.

In sweeping their most important series in years, the Mets buried a rival and sent a resounding message to the rest of the National League.

"We're legitimate," Collins said. "This is not a fluke."