The Dynamo (11-10-7) snapped a four-game winless streak and moved past Union (10-10-9) in the Eastern Conference playoff picture. Philadelphia extended its winless streak to five matches, scoring just once in that stretch.
Clark flicked a header off a free kick from Brad Davis for his third goal of the season. Tally Hall got his seventh shutout of the season without having to make a save.
The Union had a goal nullified in the 30th minute when Amobi Okugo was called for being offsides.
Philadelphia leading scorer Jack McInerney entered as a substitute for Danny Cruz in the 61st minute but went scoreless for his 12th consecutive game.
Dynamo manager Dominic Kinnear and midfielder Boniek Garcia both missed the game while serving suspensions.