The Australian combination of Chris Guccione and Marinko Matosevic downed Jeong Suk-Young and Seol Jae-Min in the doubles rubber, 4-6, 6-1, 6-4, 6-2 to clinch the Asia-Oceania second round tie.
The 28-time winners Australia will now bid to return to the Davis Cup elite group via the playoffs in September.
Bernard Tomic and Matthew Ebden gave Australia a 2-0 lead over the Koreans with straight sets wins in the opening singles on Friday.
The dead rubber reverse singles will be played on Sunday.