Andres Romero also scored for Montreal (0-3-2), which picked up a point for a second week in a row but remains without a victory under new coach Frank Klopas.
Romero scored only five minutes in to the game. He was set up when Heath Pearce recovered a ball and Felipe slipped it to the Argentine midfielder for a shot off the far post.
Felipe, Romero, Justin Map and Marco Di Vaio all had chances that either missed the net or were stopped by Luis Robles.
Then New York's Lloyd Sam got a cross past Heath and Steele beat defender Eric Miller to the ball to nudge it across the line in the 31st.
Only three minutes later, Di Vaio's weak cross-field pass was picked off by Steele, who sent it to Luyindula breaking in on the right to score for a second game in a row.
The Red Bulls wasted a chance for a third goal in the 48th when they were given a penalty after Matteo Ferrari got an arm around Bradley Wright-Phillips in the area, but Luyindula hit the post from the spot.
Felipe tied it when he played the ball to Justin Mapp on the right side, then went to the net to head in his first goal of the season.
The Red Bulls had to draw on their bench as several of their starters sat out.
Forward Thierry Henry, who has seven goals in four games against Montreal, and defender Jamison Olave weren't in the lineup because both have health issues playing on artificial turf.