The Chicago rookie saw his hat trick matched by Bradley Wright-Phillips, but the visitors still went home with the points.
Harrison Shipp opened the scoring with a controversial fourth-minute goal. As Shipp unleashed his shot, Mike Magee ran across Luis Robles' line of sight in an offside position. Assistant referee Brian Poeschel raised his flag as the ball was played, but then brought it back down and the goal stood.
Despite their protests, the Red Bulls wasted no time bringing proceedings back to level terms. Eric Alexander's cross to the far post was emphatically headed in by Tim Cahill to make it 1-1 before the game was six minutes old.
New York took the lead in the 39th minute with a goal from the in-form Bradley Wright-Phillips. Thierry Henry picked up a loose ball in midfield, glided past Jhon Kennedy Hurtado and crossed over to set up Wright-Phillips' powerful finish.
Chicago wasn't out of it, though, and roared into an impressive 5-2 lead in the second half. Quincy Amarikwa scored in the 49th minute, and then Shipp added two in five minutes to give the rookie his first career hat trick.
Patrick Nyarko put in the fifth in the 64th minute, launching an astonishing chip over Robles, and it looked like Chicago would run away with the game.
Wright-Phillips had other ideas. The English striker was again the man putting his team on the board, scoring in the 67th and 78th to bring his team within a goal of an equalizer, and almost did it himself with a bicycle kick attempt in stoppage time.
Chicago moves from the bottom of the table with its first win of the season and now boasts a 1-2-6 record. New York is now 3-3-5 and occupies fifth place.