Magee converted from just inside the penalty box in the 50th minute after the Rapids' Drew Moor was given a red card for delivering an elbow to the face of Marcelo Sarvas.
The victory enabled the Galaxy (2-0-1) to pull ahead of Vancouver and FC Dallas for first place in the Western Conference with 10 points.
The Rapids (0-3-1) will try again for their first 2013 victory March 30, when they host Portland.
Notable deaths of 2014 [PHOTOS]
UPI horse racing roundup