A penalty was called in the 38th minute when Crew defender Eric Gehrig was whistled for a blocking a shot with his upper arm. Despite putting up a strenuous argument, Gomez was awarded the shot.
The Philadelphia midfielder used a chip shot down the middle, fooling Columbus goalkeeper Andy Gruenebaum, who had committed to the right.
Philadelphia (1-3-1) collected its first win of the season, despite managing just three goals through five games this season.
Columbus (2-3-0) lost its second straight.