In a battle for the National League East lead, Washington handed the Braves their fifth consecutive setback.
Atlanta, however, closed within 4-3, with Matt Diaz driving in a run on a third-inning single and then producing a two-run double in the fifth.
Washington then took control in the seventh against starter Braves' Tim Hudson (3-2).
Hudson walked pitcher Chien-Ming Wang with two out and went on to load the bases on a double by Stephen Lombardozzi and another walk to Bryce Harper.
That brought up Zimmerman, who doubled deep to center on an 0-2 pitch.
Wang, who had been on the disabled list since the start of the season with a hamstring pull, made his first appearance of the campaign. He got the win by throwing three innings of one-run relief.
Celebrity Families of 2014 [PHOTOS]