Trailing 3-1 in the fourth inning, the Nationals scored five times to grab control of the contest and went on to clinch their three-game series against the Braves.
Jonny Gomes walked to lead off the fourth and Ian Desmond and Wilson Ramos each singled to load the bases with none out. Gomes came in to score on a fielder's choice and Ankiel followed by blasting a 2-0 pitch over the right-center field wall for a grand slam.
The Nationals' center fielder homered twice in Monday's 5-3 win over the Braves.
Desmond went 2-for-3 with three RBI, including a two-run homer, for Washington Tuesday.
John Lannan (8-7) earned the win despite allowing nine hits over 6 2/3 innings. He gave up three runs to go with one walk and eight strikeouts.
Atlanta's Derek Lowe (6-10) lasted only four innings and was lit up for eight runs (seven earned) on 10 hits.
Michael Bourn and Jose Constanza each had two hits and an RBI for the Braves.