NYCFC held on in 8½ minutes of extra time, which included Ronald Matarrita sent off with a red card.
Right after NYCFC went a man down, Tom Barlow of the Red Bulls missed an opportunity from the goal line when he couldn't get the redirect.
The Red Bulls scored in the 10th minute when local product Alex Muyl made a nice move to get inside the box and slot the ball inside the post. It was his third goal but first since mid-March.
A penalty kick by Maximiliano Moralez, his seventh, tied the game late in the first half.
The Red Bulls won the first meeting 2-1.