Soto, Washington's lone All-Star who could be traded by the end of the month, hit a solo shot in the eighth inning to extend his on-base streak to a career-high 26 games.
''It had been a long time, but finally we did it,'' Soto said. ''It feels great.''
The Nationals haven't dropped 10 in a row since an 11-game skid that spanned the 2008 and 2009 seasons. At 31-63, they have the worst record in the majors at the All-Star break.
Washington hadn't scored five runs in a game since an 8-7 loss to Pittsburgh on June 29, a loss which started the Nationals' 1-15 slide entering Sunday.
''There's still a lot of things that we need to clean up to really get better and compete every day and play consistent,'' Washington manager Dave Martinez said. ''We're going to work on those things a lot this next half, as we've been doing. I'm happy to go into the break with a big win.''
The Nationals did much of their damage against starter Spencer Strider (4-3) in the second. Ehire Adrianza lined a two-run single to center. Robles followed with his second homer of the season, a fly to left that just sailed into the visitor's bullpen.
Adrianza added an RBI groundout in the fourth against Strider, who allowed five runs in four innings while striking out four.
Maikel Franco's RBI single in the sixth made it 6-3.
Steve Cishek (1-2) pitched 1 2/3 scoreless innings, stranding the potential trying run at second in the fourth inning.
After a doubleheader Wednesday snarled its rotation, Washington opted for a bullpen game. Erasmo Ramirez started and worked three scoreless innings, allowing one hit and striking out two.
''He really picked us up,'' Martinez said. ''We never expected him to go three innings and he gave us three strong innings. When he came in after the (third) inning and he looked at me and joked around and said, `I think I have two more,' and I said, `You do for real?' and he goes, `No.'''
Jordan Weems entered in the fourth and allowed four hits in a span of five batters, including RBI doubles by Matt Olson and Adam Duvall, before yielding to Cishek.
''Those bullpen games are rough where they keep cycling guys in,'' Atlanta manager Brian Snitker said. ''It's not a sustainable thing, but when you have to do it, sometimes it's hard when you're getting different looks at guys. They did a good job.''
Nationals: DH Nelson Cruz (quad tightness) was out of the lineup for the second consecutive game. ... Washington recalled RHP Cory Abbott from Triple-A Rochester and optioned him back after the game. Abbott did not pitch Sunday. The Nationals optioned RHP Hunter Harvey to Rochester before the game. Harvey was 0-0 with a 3.18 ERA in seven games. ... RHP Victor Arano (left knee inflammation) threw a scoreless inning with two strikeouts Saturday in his second rehabilitation appearance for Rochester.
Snitker will manage the National League in Tuesday's All-Star game in Los Angeles by virtue of the Braves' appearance in last year's World Series. His son, Houston Astros hitting coach Troy Snitker, will be on the AL staff.
''It's one of these things just like the World Series was: You're never guaranteed to do that again,'' Snitker said. ''We're going to suck it up and enjoy everything about it. It's a great experience for my family to do something like that as a family. Not a lot of people get to do that.''
Braves: Atlanta returns home after the All-Star break to begin a three-game series Friday against the Los Angeles Angels. The Braves and Angels have not met since 2017.
Nationals: Washington begins a three-game series Friday at Arizona. The teams split a four-game set at Nationals Park in April.
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