The Premier League team had a helping hand from Philadelphia defender Ethan White, who headed the ball into his own in the first half as Palace emerged victors at PPL Park.
Friday's friendly win against MLS opposition in the United States was Palace's second in the lead up to the 2014-15 campaign after their thumping 14-1 victory in Austria that was followed by a 2-2 draw with the Columbus Crew on Wednesday.
Palace have one match remaining in the USA - a game against Richmond Kickers - before heading home to England for a friendly fixture against Brentford and their Premier League opener on August 16.
Manager Tony Pulis made one change to the starting XI that lined up against the Crew earlier in the week, with Marouane Chamakh coming in for striker Glenn Murray against the Union - fifth in the Eastern Conference standings.
Palace stormed out of the blocks in Philadelphia, dictating possession early and forcing goalkeeper Andre Blake into a number of saves.
Their dominance was rewarded with the opening goal in the 20th minute, albeit fortuitously.
A cross was whipped into the box - intended for Chamakh - but White rose above the former Arsenal man, only to loop the ball over his own goalkeeper.
That goal proved to be the match-winner after both teams failed to find the back of the net during a disrupted second half due to wholesale changes.
