Morales was breaking toward the goal down the middle when Alvaro Saborio chipped him a pass, which he headed into the net for his first goal of the season.
Nick Rimando made five saves as RSL (3-3-2) bypassed Chivas for second place in the Western Conference with 11 points.
Dan Kennedy turned aside four shots for the Goats (3-3-1).
Ron Burgundy interviews Peyton Manning on SportsCenter
Florida bear attack: Black bear mauls woman's face