Fister pitched eight shutout innings, and Anthony Rendon had three hits and two RBI for the Nationals, who earned a rare 3-0 victory over the Braves on Saturday night.
Washington took a half-game lead over Atlanta in the NL East after dropping the first two games in the series. Ryan Zimmerman also drove in a run for the Nationals.
Coming off his second loss of the season, Fister (6-2) allowed five hits with three strikeouts and one walk.
"He controlled the strike zone," Nationals manager Matt Williams said of Fister, who allowed two hits in the first inning but just three over his final seven. "He wants to stay in rhythm. He works fast anyway. Just because somebody gets on, he doesn't want to change that."
Braves starter Julio Teheran (6-5) struck out a season-high 10 batters. He allowed three runs and seven hits in seven innings.
Atlanta had won five straight against the Nationals, seven of eight this season, and 20 of 27 since the start of the 2013 campaign.
"It's something positive for us now," catcher Jose Lobaton said. "We're going to sleep fresh and be ready. Be ready because we've got to tie this series and keep going."
Lobaton scored two runs and helped direct traffic for Fister from behind the plate. Washington's starter didn't need much help with the work-fast game plan.
"That's the game as a pitcher," Fister said. "You control the game, and they react to you."
Rafael Soriano pitched the ninth for his 16th save.
Rendon's RBI single in the third gave Washington its first lead of the series and his run-scoring double in the seventh made it 3-0. Both of those hits came after Fister's sacrifice bunts moved a runner into scoring position.
Braves catcher Evan Gattis extended his major league-leading hitting streak to 20 games with a sixth-inning single.
Fister and Teheran lived up to the hype and locked up in a pitchers' duel.
Fister, who has won six of seven starts, has allowed two runs or fewer in seven of nine outings this season.
Atlanta had runners on the corners in the first inning after back-to-back one-out singles, but Fister fought back. He got out of the jam and started a streak of nine straight batters retired. The 6-foot-8 righty didn't allow another hit until the fifth inning in front of a sellout crowd.
"He's funky," said Freddie Freeman, who had one of Atlanta's five hits. "He's a big guy. He seems like he's releasing the ball right in front of your face.
"He's so quick he makes you want to kind of rush things to get things going."
While Washington's battery worked together cohesively, Gattis and Teheran struggled with their approach. Constant changing of signs led to Teheran frequently stepping off the mound during his outing. He struck out the side in the fifth inning, but grew frustrated as the game progressed.
"That's when the frustration (began) because I wanted the pitch that I was thinking, and I wasn't on the same page," Teheran said.
After walking Adam LaRoche in the sixth, and with a 1-0 count on Zimmerman, Teheran again shuffled around on the mound. This time he inadvertently stepped toward home plate and was immediately called for a balk.
Two pitches later, Zimmerman's single drove home LaRoche.
"After I did the dumb move I wasn't surprised that they called it because I knew that I did something wrong," Teheran said.
Zimmerman entered Saturday batting .197 since returning from the disabled list on June 3.
"He's close," Williams said of the third baseman-turned left fielder. "He's seeing it good, he's swinging it good, he's making good contact. The results haven't been there."
Justin Upton went 0-for-3 in his return to Atlanta's starting lineup. The left fielder missed three games due to dizziness caused by "a real bad case of allergies," Braves manager Fredi Gonzalez said. ... Fister improved to 2-0 against Atlanta, having won his previous start last season with Detroit. ... RHP Ervin Santana (5-4, 4.12) will pitch the series finale for Atlanta on Sunday against RHP Tanner Roark (6-4, 2.85).