Moreno's first goal this season created a 1-1 tie in the 56th minute. His second came in the 66th minute, making United 2
1 in its last three outings.
FC Dallas led 1-0 on a goal by Andre Rocha in the 28th minute.
The Hoops (1-5-1) have lost two in a row and have not won since a 3-2 victory April 19 against Toronto FC.
D.C. United outshot FC Dallas 8-3.