The Braves, who have dropped 10 of 15, saw their lead in the NL wild card race shrink to one game over St. Louis with three games remaining for both clubs. That's because the Cardinals won at home over the Cubs, 3-2, Sunday.
Atlanta hosts the NL East-champion Philadelphia Phillies, while the Cardinals travel to Houston to conclude the season.
Ross Detwiler (4-5) scattered four hits and walked two over six innings for Washington, which finished the season with a 44-36 record at home. Henry Rodriguez, Tyler Clippard and Drew Storen each tossed a perfect inning to preserve the shutout.
"We're playing against teams that are playing meaningful games and we're playing good baseball so I think that's the most important thing," said Nationals third baseman Ryan Zimmerman.
Mike Minor (5-3) gave up a solo home run to Ramos among six hits in 4 2/3 innings to suffer his first loss since May 31.
"All the pressure is on St. Louis, because if they don't win, they can't go anywhere," Minor said. "Even if we do lose, they have to win."
The Braves wasted a bases-loaded, no-out opportunity in the third and failed to score with runners on second and third in the fifth.
Washington, which stranded a runner in scoring position in each of the first three frames, took the lead in the fourth on Ramos' drive to left field.
Morse followed a single by Ryan Zimmerman by smashing his 29th home run to right field off Cristhian Martinez, extending the Nationals lead to 3-0 in the seventh.
Storen picked up his 42nd save of the year...Atlanta completed the road portion of its 2011 schedule with a 42-39 mark...David Ross had two of the Braves' four hits.