The meanings of these two words seem the same, but their spellings are very different.
Something is universal if it is present everywhere. Something is pervasive if it has a tendency to spread through everything.
Describing something as 'universal' suggests an absoluteness to its widespread presence, as if it perhaps has always been that way, whereas describe something as 'pervasive' may refer to something that has infiltrated something else over a period of time, perhaps unexpectedly.
They have completely different origins: universality comes from "universe" meaning "all things", whereas "pervasiveness" comes from the verb "to pervade" meaning to diffuse through something.
Something that is universal is something affecting, or done by all people or things in the world or in a particular group. Universality can also be used to mean "applicability on every cases."
Something that is pervasive is something spreading widely throughout an area or a group of people.