Blanco also had an assist, and the Fire came from behind twice in the Major League Soccer contest.
Van den Bergh opened the scoring in the 10th minute, cashing in on a bungled clearance attempt by the Fire defense.
The Fire tied it, 1-1, on a penalty kick in the 54th minute -- with Blanco beating Red Bulls goalkeeper Ronald Waterreus for his third goal of the season.
Angel put New York ahead, 2-1, with his 15th goal of the season on a penalty kick. But Gonzalo Segares drew the two teams even with his first goal of the season -- also on a free kick -- on a feed from Blanco.
The tie preserved New York’s third-place standing in the East, one point ahead of Kansas City. The Fire retained its hold on the eighth and final playoff spot.
Chicago travels to Dallas for a game Thursday, while New York will be at home vs. New England Saturday.