Fister (11-3) allowed one unearned run and six hits in 7 1/3 innings. He struck out seven and reduced his ERA to 2.49.
In his first season with Washington, Fister has made a positive impression with his new team by working rapidly and going after opposing hitters. The technique confounded the Mets and provided the Nationals with plenty of time to take their hacks against New York starter Jonathon Niese (5-8).
"It's no coincidence that I feel like a lot of runs get scored when Doug pitches," LaRoche said. "I think it's a matter of really quick innings. He's pitching to contact, guys are on their toes, and there's a lot of action. Seems like when he's pitching, we're out there for 30 minutes on defense and spend two hours in the dugout."
The Mets, who had faced Fister only once previously, seemingly weren't prepared for his rapid-fire style.
"He works real quick, throws a lot of strikes, doesn't walk anybody," New York manager Terry Collins said.
LaRoche hit a two-run drive in the first inning and a solo shot in the eighth, his 23rd career multihomer game. Espinosa went deep with two on in the sixth and Anthony Rendon hit two doubles to help NL East-leading Washington increase its lead over sputtering Atlanta to four games.
Niese gave up a season-high six runs on eight hits in six innings. It was only the second time in his last 25 starts the left-hander yielded more than three earned runs.
Niese is 0-4 with a 5.76 ERA in four starts since coming off the disabled list with a left shoulder strain.
"It seemed like when I didn't feel 100 percent, that's when I was pitching best," Niese said. "My arm feels a lot better so I've got to figure out how to pitch with that."
Washington got all the offense it needed in a three-run first. Rendon doubled with one out, Jayson Werth hit an RBI single and LaRoche followed with his 14th home run.
"It's certainly nice to get that," Fister said. "I've still got to go out there, still got to put up a zero and get our guys back in to hit."
Washington leadoff hitter Denard Span singled in the third to extend his streak of games reaching via a hit or walk to 32.
Mets: Collins said he expects RHP Daisuke Matsuzaka (right elbow) to throw off a mound by next week and to make a rehabilitation appearance soon after that. Matsuzaka, who was placed on the disabled list July 26, is 3-3 with a 3.87 ERA.
Nationals: Werth was pulled in the seventh with a shoulder strain. "Jayson's got a shoulder that's been bothering him a little bit. Tonight he was a little tight in his neck," manager Matt Williams said.
Mets: Rookie Jacob deGrom (6-5) seeks to win his sixth straight start when New York and Washington meet Thursday afternoon to close out the three-game series.
Nationals: Washington will start RH Jordan Zimmermann (7-5), who hasn't given up a home run at home in nine games since April 9.
Williams said he had too much to do as a player to be a scoreboard watcher.
"I couldn't afford to. I wasn't good enough," he said. "I didn't have time for it."
He's not checking out the out-of-town scores now, either.
"There's no reason to see what anybody else is doing because we're trying to take care of our business today," he said. "If we win today, the position that we're in, there can't be any movement."