The score was tied 1-1 when Santos, subbing for starter Sherjil MacDonald, struck in the 83rd minute on a through pass from Daniel Paladini, who had earlier scored to erase a 1-0 Chicago deficit.
Santos sealed the victory 7 minutes later with the tap-in of a Jeff Larentowicz header in the box.
The Fire broke a winless drought to begin the season, improving to 1-3-1.
Jamison Olave scored for the Red Bulls (1-3-2), who are winless in 10 all-time trips to Chicago.
Notable deaths of 2014 [PHOTOS]