Alex de Minaur and Jordan Thompson won their singles competition to send the 28-time champions through.
Thompson got Australia going with a 4-6 7-5 6-3 comeback win over Tallon Griekspoor.
The pair traded early breaks before Griekspoor managed to secure a 4-2 lead and held on to take the first set.
Thompson ranked 84th in the world, improved in the second set breaking his opponent at a crucial moment at 6-5 to equal the contest. The 26-year-old rolled from there staving off a late comeback bid to put Australia in the driving seat.
With the momentum firmly on his side, Alex de Minaur had to battle past Botic van de Zandschulp 5-7 6-3 6-4 to put his side in the semifinal.
The Dutchman, Van de Zandschulp, in an almost repeat of the first match, took the first set by breaking De Minaur on his third attempt. The tide quickly turned in the second stanza when De Minaur converted on break-point chances in the first and the final game to draw himself level.
The two then left everything on the court in the final set, trading sublime shots to take in the crowd’s applause.
Van de Zandschulp then handed De Minaur a break at the wrong time and the Australian gleefully accepted the gift to seal the tie.
Australia, after their win over the Netherlands, will now take on either six-times winners Spain or Croatia for a place in Sunday’s Davis Cup final.