After Columbus' Eric Gehrig was whistled for a handball in the penalty box, Gomez converted and the Union (1-3-1) held on for their first win this season.
Toronto FC (0-4-0) is the only remaining winless club in Major League Soccer.
It was the second consecutive shutout for Zac MacMath following a scoreless draw with the Vancouver Whitecaps two weeks ago.
Philadelphia played without midfielder Roger Torres (knee surgery) and forward Danny Mwanga (rib contusion). Captain Danny Califf, its central defender, was scratched just before kickoff with a hamstring strain and replaced by rookie Raymon Gaddis.
The Crew (2-3-0) have lost two straight.
(Copyright 2011 Philadelphia Union. Reprinted by permission)