D.C. (14-10-5) moved into fourth place in the Eastern Conference, one point ahead of Houston and two ahead of Columbus.
Philadelphia (7-14-6) remained ninth in the East, one point behind New England. The Union's stretched their winless streak to eight matches, falling to 0-4-4 since beating the Revolution 2-1 on July 29 - and have scored just four goals in that span.
United scored after Chris Pontius approached the box and drew Union goalie Zac MacMath out of the goal. Pontius passed it to Pajoy, who stopped the ball and sent it into the wide-open net for his seventh goal of the season - and second since being traded from Philadelphia to D.C. on Aug. 16.