"I don't think we played very well," Norwegian manager Delia said. "Offensively we played very well but defensively we looked very tired. We always were a step behind.
"We have to give full credit to Philadelphia with all the problems they have had. They made it hard for us. But we've kept going all season and here we are again."
Philadelphia's Nathan Harriel nodded a header over the crossbar in the 87th minute, a heartbreaker just before the NYCFC counterattack delivered the winner.
Philadelphia placed 11 players into MLS Covid-19 protocol on the eve of the match, including two goalkeepers and most of the backline, leaving the squad with only 17 players for a workout.
The Union added three players under extreme hardship rules, but the short-handed side walked onto its home pitch clearly unfancied despite a better regular-season record than City.
Philadelphia seized the lead in the 63rd minute when Hungarian midfielder Daniel Gazdag lofted a centering pass into the box and New York City's Alexander Callens, a Peruvian defender, deflected the ball into his own goal.
Just as Union supporters were raising their volume, City answered with the equalizer in the 65th minute off a right-footed volley by Argentine midfielder Maxi Moralez.
Union goalkeeper Matt Freeze, a hometown product who usually serves as a third-string reserve, made a diving save in the 76th minute to keep his side level into the dying minutes.