Joel Lindpere and Markus Holgersson also scored for the Red Bulls (7-3-1), who won their fourth match in a row and moved into first place in the Eastern Conference with 22 points. Sporting Kansas City is one point behind New York.
Lionard Pajoy scored two goals as the Union (2-6-1) dropped their third straight despite scoring twice for the first time this season. They entered the match with only five goals, tied with Chivas USA for last in the league.
Philadelphia tied the match at 1 in the 31st minute on Pajoy's first goal before midfielder Freddy Adu was ejected in the 44th for diving in the box - his second yellow card of the match.
Still, Pajoy put the short-handed Union ahead 2-1 in the 46th minute.
Holgersson tied it at 2 in the 68th on a header following a perfect corner kick from Brandon Barklage.
Cooper's go-ahead goal was his ninth of the season, tying him with teammate Thierry Henry, who was out with a right hamstring strain. San Jose's Chris Wondolowski leads the league with 11.
The Union played without defender and captain Danny Califf, who has been battling a left hamstring strain.
(Copyright 2011 Philadelphia Union. Reprinted by permission)
