Singles wins for Botic Van de Zandschulp and Tallon Griekspoor sparked a party amongst an army of orange-clad Dutch fans inside the Jose Maria Martin Carpena arena.
Australia now have the opportunity to avenge last year's final defeat by Italy after world number one Jannik Sinner inspired the holders to a 2-1 victory over Argentina.
Defending champions Italy moved into the Davis Cup final after a 2-0 win over Australia on Saturday as Jannik Sinner defeated Alex de Minaur in straight sets to follow up Matteo Berrettini's victory over Thanasi Kokkinakis.
Jannik Sinner spearheaded Italy's charge towards a second successive Davis Cup title with a 2-0 victory over the Netherlands in the final at the southern Spanish city of Malaga on Sunday.
Australia booked their place in the Davis Cup semi-finals as doubles pair Matthew Ebden and Jordan Thompson clinched the deciding rubber against the United States on Thursday.
Jasmine Paolini put on a tennis masterclass to steer Italy to a fifth Billie Jean King Cup title as she beat Rebecca Sramkova 6-2, 6-1 in the second singles rubber to wrap up a 2-0 win over Slovakia in the final on Wednesday.
Italy returned to the Davis Cup final after a gap of 25 years as Jannik Sinner beat Novak Djokovic in both singles and doubles to secure a 2-1 victory over Serbia on Saturday that earned the 1976 champions a title clash with Australia.
Poland will face Italy in their first ever Billie Jean King Cup semi-finals after beating the Czech Republic 2-1 in a hard-fought tie that ended in the early hours of Sunday.
'In some ways it is good, maybe, if that was my last match because I lost my first match in the Davis Cup and I lost my last one. We close the circle'
Novak Djokovic steered Serbia into the Davis Cup semi-finals with a straightforward 6-4 6-4 win over Britain's Cameron Norrie to give his team a winning 2-0 lead on Thursday.