Mapp set up reserve forward Jack McInerney for the tying score with a short chip into the penalty box area, then converted a feed from Sebastien LeToux for the Union's match-winner, a left-footed drive from 14 yards out.
Philadelphia (5-11-5) had been winless in its previous six matches (0-3-3) and won for just the second time on the road this season. The Union hadn't won since May 29.
New England (5-12-3) lost its third straight and has been outscored 8-2 during the skid.
Philadelphia scored both second half goals as New England played the final 49 minutes a man down. New England defender Cory Gibbs was red-carded by referee Hilario Grajeda in the 41st minute for a flagrant tackle of Philly midfielder Eduardo Coudet.
New England took a one-goal lead into halftime - for just the fourth time this season - with the help of some energetic play by Shalrie Joseph and Ilija Stolica in the 31st minute.
Marko Perovic took a corner kick from the left wing that bounced around the penalty box area and off Joseph's chest. Stolica, falling to the ground amid a scrum of players, got his left foot on the ball and tucked it into the left corner of the net, past Philly goalie Chris Seitz.
The Union managed just two shots, none on goal, and had just one corner kick (in the 28th minute) against New England reserve goalie Bobby Shuttleworth, making just his third appearance and second start in the absence of starter Matt Reis (bad back).
New England nearly had a second goal as striker Sainey Nyassi ripped a left-footed drive off the left goalpost in the 36th minute.
(Copyright 2010 Philadelphia Union. Reprinted by permission)