Ryan Church struck out and Hanrahan (0-1) intentionally walked David Wright and Carlos Delgado to load the bases. Hanrahan then bounced the first pitch to pinch-hitter Brian Schneider, and Easley raced home with the winning run.
Six Mets relievers combined to throw seven scoreless innings with Jorge Sosa (2-1) getting six outs to earn the win.
The Nationals wasted an opportunity to go in front in the 11th when former Mets prospect Lastings Milledge grounded into an inning-ending fielder's choice with two runners on. Nick Johnson also popped out with two on to end the 13th.
New York has won three straight and went 6-3 on its first homestand of its final season at Shea.
Johnson hit a two-run homer for the Nationals, who managed just five hits and have lost 12 of their last 13 games. Washington entered the day last in the NL in batting average and hits.
The punchless Nationals wasted a terrific effort by Long Island native John Lannan, who had a career-high 11 strikeouts in his first start at the Mets' longtime home. He allowed just one run and three hits in six innings.
Lannan became the first rookie left-hander to record 10 or more strikeouts in a start without a walk since Noah Lowry did it for the Giants against the Mets in San Francisco on Aug. 20, 2004, according to the Elias Sports Bureau.
The Mets stayed close behind their own hometown pitcher, Brooklyn-born Nelson Figueroa. The journeyman right-hander struck out seven in seven innings, allowing two runs and three hits.
Figueroa, who grew up a Mets fan, earned his first major league win since 2003 last Friday when he beat Milwaukee in a home start.
Lannan handed a 2-1 lead over to the Washington bullpen and the Mets rallied in the eighth. Church reached on second baseman Ronnie Belliard's two-out error and went to second when Luis Ayala walked Wright.
Delgado, who struck out in his first two at-bats, then hit an RBI single off Nationals closer Jon Rauch.
New York also had some opportunities to end the game before the 14th. Angel Pagan lined out with two on to end the 10th and Wright grounded into an inning-ending double play with two on in the 12th.
It was the longest game at Shea Stadium since the Mets beat the Phillies 9-8 in 16 innings on May 23, 2006.
New York paid tribute Thursday night to the first team that took the field at Shea.
Former Mets Ron Hunt, Jack Fisher and Tim Harkness were on hand to change the sign in left-center field counting down the number of regular-season games remaining at the club's creaky home. Harkness recorded the Mets' first hit at the stadium, Hunt scored the team's first run and Fisher started New York's 4-3 loss to the Pittsburgh Pirates.
The Mets' new home, Citi Field, already is a prominent part of the skyline beyond the outfield wall at Shea.
Lannan allowed a leadoff single to Jose Reyes in the first and Church followed with an RBI double into left-center field. He settled down after that, retiring 16 straight before Reyes singled again with one out in the sixth.
Lannan nearly got a hit in the fifth but Figueroa reached behind his back to spear the line drive up the middle.
