After Dominic Oduro had brought the Fire back on level terms following Michael Farfan's opener for the Union, Guatemalan Ruiz struck from 35 yards out, collecting a clearance from his own free-kick and volleying over Chicago keeper Jon Conway.
The victory moves Philadelphia a point clear of the New York Red Bulls who, without injured French striker Thierry Henry, were held to a 2-2 draw at the Houston Dynamo.
The assist was Beckham's sixth of the season but he is now set to miss the Galaxy's midweek match-up with Houston as he will be playing in former Manchester United team-mate Gary Neville's testimonial game in England.
Dallas and Real Salt Lake's game on Sunday was delayed, in the 83rd minute, for one hour 40 minutes due to a rain storm but finished 0-0.
