Chicago improved to 5-1-1, having allowed only three goals all year. United fell to 2-5-0 and is in last place in the East.
Mapp scored in the 38th minute off a header directed his way from Chris Rolfe. It was Mapp's first goal in two years.
Blanco beat United goalie Zach Wells with a shot from 25 yards in the 62nd minute.
Busch needed to make just two saves. His four shutouts lead MLS.
2014: The Year in Music [PHOTOS]