Casey scored in the 35th minute, with Sebastien Le Toux picking up his league-best 11th assist, and in the 75th. He trails Jack McInerney by one goal for the team lead.
The Union (10-7-7) improved to 3-1-1 in their last five games. Philadelphia goalkeeper Zac MacMath earned his eighth shutout of the season.
D.C. United have dropped three of their last four and fell to a league-worst 3-16-4 overall and 0-8-3 on the road. They're the only club without at least one road victory.
Philadelphia is 4-3-2 against D.C. United overall and 2-0-0 this season.