Alvaro Saborio struck first as DC earned a half-time lead, but a rousing second-half display, courtesy of goals from Thomas McNamara, David Villa and Kwadwo Poku, saw them respond in style after losing to rivals New York Red Bulls last time out.
Twenty-four minutes elapsed before the first real chance came about following a tentative opening, and it was for United as Saborio failed to beat Bill Hamid from six yards out.
However, the DC hitman atoned for that miss on 36 minutes when Chris Rolfe intercepted a loose ball before setting up his strike partner to finish from an acute angle.
The hosts looked certain to level up before the break, but Bobby Boswell threw himself in the line of fire to deny Villa's effort on the line as the visitors earned a slender half-time lead.
New York maintained that momentum throughout the break and drew level on 51 minutes when McNamara tapped home from a matter of yards.
City were unfortunate not to then go ahead as Poku - who set up the equaliser - saw his bid for a second rebuffed by the woodwork after the hour mark.
Saborio and Perry Kitchen both missed gilt-edged opportunities from close range, before the duo were made to pay for their profligacy.
On 81 minutes, Villa collected Andrea Pirlo's pass before stroking past Hamid from inside the box, while Poku added a third in the dying minutes of normal time as the Sky Blues clinched all three points. body check tags ::