Juvan defeated Ajla Tomljanović in two sets, while Zidanšek overcame Daria Saville with a similar result.
Although Australia claimed a point in doubles, with Kimberley Birrell and Storm Hunter defeating Veronika Erjavec and Ela Nala Milič, Slovenia's strong start positions them well in the competition.
Slovenia will face Kazakhstan on Friday, featuring Elena Rybakina, the world's fourth-ranked player.