A new cultivar of Phlox plant named, ‘Pink Parasol’, that is characterized by its flower petals that are distinctly bifid with a deep cleft, its flowers that have a distinct center eye that is white in color and remains persistent for the life of the flower, its striae that are inconspicuous and if visible form 2 indistinct narrow dark violet lines at the base of each petal lobe, its flowers that are medium purplish pink in color with the pigments persisting or darkening slightly as the flowers age, its flowers that cover 90% to 100% of the plant at peak bloom, and its broad mounding habit that does not spread into an indeterminate groundcover like most moss phlox.