The Red Bulls picked up three points for the first time in 2014 with a victory over their nearest rivals.
Thierry Henry scored the first goal of the game in the 57th minute. Eric Alexander's cross back from the endline caught Union defender Aaron Wheeler out of position, and the Frenchman had time to pick his spot and shoot.
The Red Bulls had a second 10 minutes later. Eric Alexander's lofted cross was headed in by Lloyd Sam, and Zac MacMath was stuck on his feet as he watched the ball go in.
The Union were handed a lifeline in the 78th minute. Ibrahim Sekagya was shown a red card for a handball in the box and former Red Bull Sebastien Le Toux converted the spot kick to make it 2-1.
The Union poured on the offense late, looking to make the advantage count - including a brief spell when Thierry Henry was taken to the sideline and New York was playing with nine - but were unable to find an equalizer.
Both teams now have 1-2-4 records, although the Union are slightly ahead in the Eastern Conference table due to superior goal difference.