Slovenia set up Billie Jean King Cup semi against Italy
Slovenia will face Group D winners Italy on Saturday.
The lowest-ranked of the 12 nations to qualify, Slovenia beat Australia in their opening match meaning victory over Kazakhstan would secure their passage.
Kaja Juvan thrashed Anna Danilina 6-1 6-0 before Zidansek took on Yulia Putintseva, knowing one set would be enough to ensure their progress to the weekend.
Zidansek duly took the opening set 6-2 before Putintseva hit back to level the match, at which point Zidansek retired in the knowledge that her country had done enough to qualify.
The last semi-final spot will be decided later on Friday with a heavyweight clash between 11-time champions the Czech Republic and 18-time winners the United States.
Canada, who wrapped up their semi-final place with a second successive 3-0 victory on Thursday, await the winners of the Czech v US tie.
