The teams will meet on Sunday at the Estádio do Maracanã, in a repeat of the 1986 and 1990 finals - the first time the same two teams will have faced each other three times in the decider.
In contrast to Germany's 7-1 annihilation of Brazil 24 hours earlier, neither Lionel Messi or Robin van Persie could help their sides break the deadlock in a goalless 120 minutes.
But Argentina rose to the occasion in the penalty shoot-out, scoring a 4-2 victory in Sao Paulo.
Argentina goalkeeper Sergio Romero saved Ron Vlaar's first penalty then made a superb diving save to deny Wesley Sneijder, allowing Maxi Rodriguez to crash home the decisive kick as his side converted all four penalties.
The game was a forgettable one as the Dutch struggled to build any meaningful attacks and completed 90 minutes without a shot on target.
Argentina were not much more adventurous and had only a handful of half-chances to their name.
The Netherlands will now play Brazil in the third-place play-off in Brasilia on Saturday.