Chicago got a chance to equalise just five minutes later from the penalty spot after Jonathan Steele handled in the area.
Chris Rolfe stepped up but could only send his effort well wide of the target.
Thierry Henry came off the bench for New York after 60 minutes and went close to an instant impact as his curling strike came back off the post.
Chicago kept plugging away and made New York pay for a string of missed chances late on with an inspired substitution of their own.
Santos was the man who made the difference, cutting inside Olave before guiding a composed finish into the corner to put Chicago ahead.
With three minutes left Santos took advantage of slack marking to tap in his second and seal all three points for the home side.