The Nationals (11-5) have won five straight.
The undermanned Mets (8-9), who were missing four Opening Day starters -- first baseman Lucas Duda (left elbow), shortstop Asdrubal Cabrera (hamstring), catcher Travis d'Arnaud (right wrist) and left fielder Yoenis Cespedes (hamstring) -- lost for the sixth time in seven games.
Bryce Harper, who hit a two-run homer in the first inning, started the 11th-inning rally with a one-out double off Josh Smoker (0-1). After Smoker intentionally walked Daniel Murphy, Jeurys Familia, who returned from a 15-game domestic violence suspension on Thursday, entered and uncorked a wild pitch that allowed Harper to advance to third.
Familia eventually walked Anthony Rendon to load the bases before walking Turner, who was activated from the 10-day disabled list earlier in the day, on four pitches. It was Turner's first walk of the season.
Enny Romero (1-0) threw a perfect 10th inning and Shawn Kelley picked up his third save with a perfect 11th.
Jose Lobaton homered leading off the fifth for the Nationals, who didn't get another hit until Harper's double.
Michael Conforto led off the game with a homer for the Mets and Curtis Granderson laced an RBI single in the fourth and a solo homer. Conforto also singled in the fifth and walked in the seventh.
Nationals right-hander Tanner Roark allowed three runs, seven hits and three walks while striking out five in 6 2/3 innings. Mets right-hander Matt Harvey, whose start was moved up a day when scheduled starter Jacob deGrom was scratched due to a stiff neck, allowed three runs, four hits and two walks while striking out two in seven innings.
NOTES: The Mets placed 1B Lucas Duda (left elbow) and IF Wilmer Flores (knee infection) on the 10-day disabled list and recalled LHP Sean Gilmartin and RHP T.J. Rivera from Triple-A Las Vegas. Rivera started at third base and went 1-for-4 while Gilmartin could start Saturday if RHP Jacob deGrom (stiff neck) is not ready. ... To make room for SS Trea Turner, the Nationals designated IF Grant Green for assignment. ... Turner did not start because manager Dusty Baker said Friday was penciled in as a rest day during his rehab.