Pagan became the first player in 55 years to take part in both feats in the same game. Despite his achievements, the Mets lost for the ninth time in 11 games.
Pagan hit the first inside-the-park home run in Nationals Park history in the fourth inning. An inning later, the center fielder's shoestring catch led to the Mets' first triple play since 2002.
Phillies shortstop Ted Kazanski was the last player to do both, on Sept. 25, 1955, for Philadelphia against the New York Giants, the Elias Sports Bureau said. That was also the last time a team pulled a triple play and hit an inside-the-parker in the same game, Elias said.
Pagan's homer came in Washington's third season at its ballpark. His second career inside-the-parker came on a drive off the center-field wall. Nyjer Morgan couldn't make a leaping grab and Pagan scampered around the bases, sliding home safely ahead of a relay by shortstop Ian Desmond.
After making an earlier diving grab to rob Roger Bernadina of an extra-base hit, Pagan started the 10th triple play in Mets history.
The Nationals put runners on first and second in the fifth and Cristian Guzman hit a sinking liner that Pagan rushed in to catch.
The runners kept going and Pagan threw home, just in case. Catcher Henry Blanco tossed the ball to shortstop Jose Reyes at second base to double off Livan Hernandez. Reyes relayed to first baseman Ike Davis to catch Morgan.
Crew chief Tim Tschida briefly huddled with the other base umpires before affirming the call.
The Mets' last triple play came May 17, 2002, against San Diego, an around-the-horn play on a groundball by Wiki Gonzalez. The last time the Montreal/Washington franchise hit into a triple play was July 28, 2002, when Vladimir Guerrero of the Expos hit a line drive to Florida third baseman Mike Lowell.
The Nationals broke a 2-all tie with a three-run seventh. Bernadina hit a leadoff double against Raul Valdes (1-1) and scored on pinch-hitter Adam Kennedy's sacrifice fly off reliever Fernando Nieve.
Guzman added an RBI triple and scored on Ryan Zimmerman's single.
Rookie Drew Storen (1-0) got the final two outs of the seventh for his first major league victory. Matt Capps got the final three outs for his major league-leading 15th save despite allowing Fernando Tatis' solo homer.
Washington got to Mets starter R.A. Dickey, whose contract was purchased from Triple-A Buffalo before the game, for two runs in the fourth.
The knuckleball specialist allowed singles to Guzman and Zimmerman before walking Adam Dunn to load the bases. Josh Willingham followed with a tying single and Bernadina had a sacrifice fly, with Pagan making a diving catch in left-center.
The Mets tied it in the sixth when Jeff Francoeur hit a bases-loaded sacrifice fly.
NOTES: Pagan's other inside-the-park homer came Aug. 23, 2009, against the Phillies' Pedro Martinez. ... Dunn returned to the Nationals lineup after missing three games with an undisclosed ailment. ... Slumping 3B David Wright was held out of the Mets lineup, which included Davis as the cleanup hitter for the first time. The rookie went 1 for 4.