In complete contrast to Germany's 7-1 annihilation of Brazil 24 hours earlier, both teams played cautious football at the Arena Corinthians and there were few chances in a goalless 90 minutes.
The stalemate continued in extra-time and it took a shoot-out to split the teams, as Argentina won 4-2 to spark scenes of celebration.
There was no option to bring on Tim Krul like the Dutch had done to great effect against Costa Rica as Louis van Gaal had already made his third substitution early in extra-time, and it was to be Sergio Romero rather than Jasper Cillessen who emerged as the hero.
Romero saved from Ron Vlaar and Wesley Sneijder and it was Maxi Rodriguez’s spot-kick which sealed Argentina's victory.
Van Gaal had been boosted ahead of kick-off by the news that Robin Van Persie had overcome an upset stomach and was fit enough to make the starting XI, but the Manchester United striker had little impact.
Aware of the madcap first half that took place in Belo Horizonte on Tuesday night, both teams were unwilling to take risks.
Van Persie's opposite number Lionel Messi could not get the game going either, mainly because he was being tightly marked by Nigel de Jong, who was a surprise starter.
Sneijder banged a volley two yards wide for the Dutch 12 minutes in, but little else of note happened for the rest of the half.
When Vlaar brought down Enzo Perez on the edge of the box, the Netherlands held their breath as Messi strode up to the ball, but he fired his free-kick straight at Cillessen.
Messi was not up to his usual best. He was dropped from corner-taking duties after a couple of wasted efforts. His replacement, Ezequiel Lavezzi found Ezequiel Garay, but he headed over after diving bravely at Vlaar's raised foot.
Javier Mascherano looked dazed following a clash of heads with Georginio Wijnaldum, but he was back in action after two minutes' worth of treatment.
Sneijder then needed treatment from the Dutch physio just before half-time after being clattered by Martin Demichelis.
Bruno Martins Indi was booked just before the half-time whistle for fouling Messi, and was replaced at half-time as Van Gaal brought on Daryl Janmaat.
Sneijder blasted a free-kick high over the bar early in the second half, before Janmaat did well at the other end to prevent Gonzalo Higuain from having a clear attempt on goal from Lavezzi’s cross.
Arjen Robben began to look more dangerous after being starved of service in the opening 45 minutes, but chances remained few and far between as the pattern of the game stayed largely the same and neither side showed too much adventure.
Lavezzi had a shot from the edge of the area blocked by Vlaar following a promising break, before the flag was raised against Van Persie as he tried to hook in a volley from Janmaat’s cross.
The flag went up incorrectly moments later at the other end as Higuain turned a first-time effort into the side-netting from a tight angle, which had some in the crowd thinking the deadlock had been broken.
When there were free-kicks in decent positions, the opportunities were wasted by both teams as poor crosses were delivered, while Cillessen had no problem in keeping out a speculative shot from distance from Marcos Rojo.
The impressive Vlaar cut out a menacing cross from substitute Sergio Aguero, before Robben was denied by a wonderful block from Mascherano as the best opening of the night came just before the whistle for 90 minutes.
The Bayern Munich winger latched on to a clever Sneijder back-heel to burst into the box past Martin Demichelis, but Mascherano covered brilliantly to slide in as the shot was unleashed.
Robben’s trickery caused further problems for the Argentina defence as extra-time began, while the introduction of Klaas-Jan Huntelaar for Van Persie as Netherlands’ third substitution took away the possibility of Krul coming on later as he had done against Costa Rica.
Gaps started to appear as legs tired, but defences continued to dominate and Janmaat cleared a cross from Rodrigo Palacio before it could reach Aguero.
Palacio had a header saved by Cillessen in the second period of extra-time and Maxi Rodriguez scuffed an effort straight at the keeper, before the drama of penalties left Argentina jubilant and Netherlands heartbroken.