Johnson struck a right-footed shot that curled into the bottom left corner past diving goaltender Jon Busch as the Timbers (2-1-3) won a second straight game.
Portland goalkeeper Donovan Ricketts made three saves in notching the shutout.
The Earthquake (2-3-2) played with 10 men after Alan Gordon was issued a red card in the 69th minute.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys