Jose Lobaton, Adam LaRoche and Scott Hairston also homered for the Nationals, who returned to .500 with two straight victories over the Rangers. Washington chased Texas starter Nick Tepesch early after scoring five runs in the first two innings and finished with 12 hits.
The Nationals' once-laboring offense has produced 24 runs and 42 hits over its last three games including Friday's 9-2 series-opening win over the Rangers.
"This was huge to build off of, to know that we can go out there and get more than five or six hits a game and just keep pouring it on," said LaRoche, whose three-run home run in the fourth was part of a 2-for-3 day. "That's what the really good teams do."
That was more than enough for Fister (3-1), who allowed two runs on four hits with six strikeouts for his third win in as many starts. He held the Rangers hitless until Elvis Andrus' one-out double in the fourth, and scoreless until the fifth.
"Pitching stops hitting, and the last two days, their guys stopped us and the guys we sent out didn't stop them," Rangers manager Ron Washington said. "Fister did his job. We worked him pretty good, but he stayed focused with the big lead and got the job done."
Out the first six weeks with a lat strain sustained during Spring Training, Fister has a 2.13 ERA over his last four starts. In those outings, Washington has scored 29 runs.
"I think there is something there," LaRoche said of the Nationals' run support when Fister pitches. "You get a guy that works quick, is a contact pitcher, not trying to strike everyone out. … Here it is, hit it, let the defense work. You're on your toes."
Fister, who is in the National League this season after spending his first five years in the American League, entered with a 5.67 ERA vs. Texas, his highest against another team with at least one start.
"I've seen a few of those guys before. There are a quite few of them that are fairly new," Fister said. "It's still a matter of going out there and executing."
Tepesch (2-1) allowed only two homers in 18 1/3 innings entering Saturday, but he gave up two the first time through the order against Washington.
Rendon, who would score three runs in the game, hammered a 2-2 sinker from Tepesch over the left-center wall for a 1-0 lead in the first. Lobaton's second home run of the season gave Washington a 3-0 lead and highlighted a four-run second inning as the Nats batted around.
Jayson Werth's two-out double, the third straight hit off Tepesch, scored Denard Span from second base. Left fielder Shin-Soo Choo botched an attempt to scoop up the ball, allowing Rendon to score an unearned run from first base.
Hairston's two-run homer in the sixth inning came as a pinch-hitter for Werth. Like LaRoche's home run, Hairston's blast came against reliever Scott Baker, who surrendered five runs in five innings.
Texas scored single runs in the fifth and sixth innings off Fister, including Rougned Odor's bloop RBI double.
Washington immediately countered with Hairston's homer, his first of the season and his 13th as a pinch-hitter, the most among active players.
Rendon, who turns 24 next month, is filling in at third base with Ryan Zimmerman rehabbing his fractured thumb at Class A Potomac. He also appears set as the long-term option at third. He displayed his defensive progress with a spectacular backhanded stop, followed by a strong throw to first for an out in the second inning before the crowd of 35,164.
"I don't know. I just threw it. It happened to go to [first base]," Rendon said.
His manager, a former All-Star third baseman, elaborated.
"That's a great play, probably the most difficult one over there," Matt Williams said. "It's the high chopper that you can't come get that you have to give on, and he goes down to his knees to stop himself and turn and throw."
Rendon struggled in May, batting .181, but he had six straight hits over the last two games before recording an out in the ninth.
"Anthony got a couple of bloop base hits in the last couple of days, and that sometimes helps you get going," Williams said.