Robles was forced into action once again before the break to deny Cristian Maidana, who had earned himself space on the edge of the box by dodging a couple of tackles.
The deadlock was finally broken in the 57th minute when Henry pulled away from his marker in the area to drill home Sam's cross from the left.
New York edged closer to victory just 10 minutes later as Sam turned from provider to finisher when he powerfully headed Eric Alexander's delivery past Wenger.
However, Philadelphia were handed a lifeline when the Red Bulls were reduced to 10 men shortly after Ibhrahim Sekagya had handled inside the box to gift the visitors a penalty.
Sekagya was forced to depart despite his protests, and Philadelphia took the chance to pull a goal back, with Sebastien Le Toux firing home the spot kick.
The visitors piled the pressure on in the closing stages, but New York held firm to secure the win at the Red Bull Arena.