Fister (11-3) surrendered just an unearned run on six hits and struck out seven over 7 1/3 innings.
The right-hander has gone at least seven innings in three straight starts and 10 of 16 this season. Washington is 12-4 in those outings when Fister toes the rubber.
Adam LaRoche homered twice and Danny Espinosa hit a three-run shot for the Nationals, who snapped a brief two-game losing streak and increased their lead in the NL East to four games over the scuffling Atlanta Braves.
Jon Niese (5-8) took the loss after getting tagged for six runs on eight hits and two walks. The southpaw is now 0-4 since returning from a stint on the disabled list with a strained shoulder.
The Nats wasted no time, plating three runs in the bottom of the first inning. Anthony Rendon clubbed a one-out double off the out-of-town scoreboard in right and scored on Jayson Werth's bloop single a batter later. LaRoche followed with a blast to right that staked the hosts to a 3-0 lead.
Ian Desmond poked a single to center with one out in the sixth and Bryce Harper drew a walk to put a pair of runners on. Espinosa then stepped in and cranked a homer out to left that doubled up the Mets, 6-0.
Juan Lagares singled to lead off the eighth and advanced to second when Ruben Tejada grounded a routine double-play ball to Rendon, who skipped his throw into second for an error. Fister struck out pinch-hitter Eric Campbell, then gave way to Matt Thornton.
Thornton, who was acquired off waivers from the New York Yankees, got Curtis Granderson to fly out to left for the second out of the frame. Daniel Murphy followed by grounding a single through the right side that allowed Lagares to race home for the only New York run.
LaRoche got the run back in the home half, however, with a long drive to center for his 15th homer of the campaign.