Doubles pair John Peers and Sam Groth gave Australia an unassailable 3-0 lead over the Czech Republic with a crushing straight sets victory in the Davis Cup World Group in Melbourne on Saturday.
Peers and Groth raced through the scratch Czech pairing of Jiri Vesely and Jan Satral, 6-3, 6-2, 6-2 in 90 minutes to deliver the tie to the Australians.
The Czechs had to win the pivotal doubles rubber to stay in the tie after losing both of Friday's opening singles matches.
But they were further disadvantaged when experienced Radek Stepanek was forced to withdraw from the doubles with injury on top of the unavailability of world number 10 Tomas Berdych for the tie.
World number 15 Nick Kyrgios conceded just seven games in reeling off a 6-2, 6-3, 6-2 win over the 157th-ranked Satral, while rookie Jordan Thompson upset Czech number one Vesely 6-3, 6-3, 6-4 in Friday's singles.
Australia, captained by Lleyton Hewitt, will now face either the United States or Switzerland in the quarter-finals of the teams competition and will have home advantage should the Americans progress.
Doubles specialist Peers is fresh off a Grand Slam title win at last month's Australian Open, while Groth reached the quarter-finals of the men's doubles in Melbourne.
Australia now lead the Czech Republic 8-1 in Davis Cup ties.
Australia have not won the Davis Cup since 2003 and only returned to the competition's top tier in 2014 after a six-year absence.