Two goals in the space of 12 minutes from Charlie Davies and Teal Bunbury cancelled out Cristian Maidana's 42nd-minute opener at PPL Park as the Revolution extended their unbeaten streak in MLS to five matches.
The Revolution, who opened the 2015 season with back-to-back defeats, are up to third in the Eastern Conference with 11 points from seven matches and only adrift of leaders New York Red Bulls on goal difference.
Sunday's defeat left the Union eighth in the East with just one win from eight games.
Philadelphia were unfortunate not to take the lead in the 16th minute after Fernando Aristeguieta's powerful effort deflected off New England goalkeeper Bobby Shuttleworth and cannoned into the crossbar.
The Union, though, took a lead into the half-time break courtesy of Maidana, who curled a long-range free-kick past Shuttleworth three minutes before the interval.
New England stepped it up a gear in the second half with two unanswered goals.
Davies - unmarked at the back post - restored parity in the 64th minute as Philadelphia's defenders were caught napping.
Substitute Bunbury completed the comeback 12 minutes later after outsprinting Ray Gaddis and poking the ball beyond John McCarthy.
Maurice Edu and Aristeguieta were both denied in frenetic finish as the Revolution held on for their second consecutive away victory.
Dairon Asprilla scored his first MLS goal to lift Portland Timbers to a 1-0 win at New York City.
Asprilla's deflected shot in the 79th minute at Yankee Stadium proved to be the winner against an injury-hit New York, who were missing stars David Villa (hamstring) and Mix Diskerud (ankle), along with Josh Williams (abductor sprain).
Portland's second win in seven outings lifted the club up to fifth in the Western Conference, while New York remain sixth in the East after a five-match winless run.
