Acosta opened the scoring in the 29th by running past the defense for a glancing header of a goal kick, cut back two defenders and sent in a shot from near the penalty spot. He added his second in the 77th on a one-on-one breakaway.
Bill Hamid made six saves for D.C. (8-12-6), which ended a two-game scoreless losing streak. United is six points behind Montreal for the final playoff spot in the Eastern Conference.
Jeff Larentowicz headed in a goal for Atlanta (16-5-6) in the 39th to tie it at 1. Atlanta had a seven game unbeaten streak snapped and sit a point behind the Supporters' Shield leader New York.
Atlanta star Josef Martinez failed to add to his MLS season record of 28 goals. With a goal, he would have set a MLS record with his 10th straight scoring game.