The Mets also lost a player in the game, however, when center fielder Andres Torres strained his left calf in the top of the second inning. Torres is day to day.
Duda went opposite field for his solo home run in the fourth, putting Strasburg on the hook for his third consecutive Grapefruit League loss. Still, Strasburg submitted his best spring outing to date, holding the Mets to just that one run over five innings. The right-hander allowed only one other hit and one walk, striking out three.
But the Mets received an even better performance from their own starter, Dillon Gee, who fired 5 2/3 scoreless innings with four strikeouts. Gee induced two double plays to hold the Nationals off the board.
"He's done exactly what we saw him do last year -- great command, changing speeds," Mets manager Terry Collins said. "He's pitched very well."
Also contributing to shutout pitching was Mets closer Frank Francisco, who has now thrown scoreless innings in consecutive games after allowing one run in each of his first four outings.
Up next: Another significant test comes Wednesday for Johan Santana, who will attempt to throw 80 pitches in the Mets' 1:05 p.m. ET game against the Cardinals in Jupiter, Fla. The game can be heard live on Gameday Audio. Including Wednesday, Santana has three more starts scheduled between now and Opening Day on April 5. Lefty bullpen candidates Garrett Olson and Josh Edgin will also make the trip to Jupiter.