The Union entered the contest having earned only two points from their first four games, but the club took the lead inside of three minutes thanks to a Jacob Peterson own goal.
Sporting answered in the 16th through Dom Dwyer, but Fernando Aristeguieta scored his third goal of the season only three minutes later, putting the visitors ahead 2-1.
That lead lasted until the first minute of stoppage time when Sporting’s Jalil Anibaba equalized before Nemeth scored a few minutes later to hand the Union their most crushing defeat of the campaign.
Philadelphia remains winless in five games this term and has earned just two points, while Sporting has collected seven points from the past three games.
Sporting goalkeeper Luis Marin had to shoulder much of the blame for his side falling behind early as he allowed Sebastien Le Toux’s corner kick to sail over his head and off the leg of Peterson, redirecting the ball over the goal line.
It was the kind of break needed by a struggling side like Philadelphia, although Union goalkeeper Rais M’bolhi returned the favor in the 16th minute.
Benny Feilhaber drove a corner kick into the box and M’bolhi stumbled as he attempted to punch it, allowing Dwyer to head the ball into the empty net at the back post.
But the Union answered quickly with another set piece. This time Le Toux curled a free kick into the box from the right wing and Aristeguieta held off his man to turn a header past Marin from 10 yards.
The hosts spent much of the second half on the front foot but were frustrated by the Union’s ability to absorb the pressure.
Dwyer had a goal ruled out for a questionable foul in the 59th, and the Union could have put the game away late when Le Toux had a shot tipped onto the post by Marin.
That save proved crucial in stoppage time as Anibaba got up and nodded the ball down through traffic and just inside the right post.
However, Sporting wasn’t done as Matt Besler’s flicked header from a Feilhaber free kick deflected off of Nemeth and into the net from close range, giving the hosts an unlikely three points.