Louis van Gaal's men overcame the USA 3-1 to book their spot in the last eight, while the South American champions got the better of Australia 2-1 to keep their hopes of glory alive.
Match preview
Cody Gakpo's hot streak in front of goal may have come to an end against the USA, but Van Gaal's effervescent wing-backs shouldered the goalscoring burden in Saturday's last-16 battle, where the Yanks failed to build on a fast start and were punished for it.
Denzel Dumfries provided identical assists for identical goals for Memphis Depay and Daley Blind in the first half, and while Haji Wright's unorthodox flick gave the USA a glimmer of hope, Blind turned provider for the in-demand Dumfries to volley home unchallenged to settle the match.
Van Gaal did little to justify his claims that the Netherlands were not a "boring" side when the USA put them under the cosh in the opening exchanges, but Oranje sure did teach their American counterparts a lesson in ruthlessness to make the quarter-finals for the third time in a row.
Indeed, the Netherlands have now reached the last eight in four of their last five World Cup tournaments - the outlier being a last-16 elimination in 2006 - and they progressed to the semi-finals in both 2010 and 2014 before miserably failing to qualify for the Russia edition.
Not since 1994 have the 2010 runners-up failed to win a quarter-final match at the World Cup, and the Netherlands' unbeaten streak in all competitions now stands at a whopping 19 matches, but something has to give when two attacking heavyweights battle for supremacy.
The script had been written for Lionel Messi to end his knockout hoodoo in his 1,000th career match, and the seven-time Ballon d'Or winner finally scored his first non-group stage World Cup goal in trademark Messi fashion against Australia, who did not go down waving the white flag.
The Paris Saint-Germain veteran found the back of the net with a low finish before Julian Alvarez robbed Mathew Ryan of the ball for Argentina's second - much to the amusement of the goalkeeper's Copenhagen rival Kamil Grabara - before Craig Goodwin's deflected strike gave Australia dreams of an improbable turnaround.
The Socceroos very nearly did the unthinkable through Newcastle United-bound teenager Garang Kuol in the final few seconds, but Emiliano Martinez produced a vital save to send Argentina through to the last eight, albeit in very nervy fashion.
Argentina most recently progressed from the quarter-finals in 2014 en route to finishing as runners-up, but they had lost their last three ties in the last eight before that in 1998, 2006 and 2010, and their hopes of glory have ended at the hands of European teams nine times in a row since the inaugural 1930 edition.
History therefore does not favour Lionel Scaloni's men, but a 13-game scoring streak in all competitions does, and La Albiceleste would do well to wrap Messi up in cotton wool as they attempt to end a barren streak in previous meetings with the Dutch.
Indeed, Argentina have failed to score in each of their last three matches versus the Netherlands, who have held La Albiceleste to two 0-0 draws in their most recent two World Cup meetings - winning the 2014 semi-final on spot kicks - but the last thing that the Qatar tournament needs is yet another goalless affair.
Netherlands World Cup form:
W
D
W
W
Netherlands form (all competitions):
W
W
W
D
W
W
Argentina World Cup form:
L
W
W
W
Argentina form (all competitions):
W
W
L
W
W
W
Team News
The Netherlands were briefly handed a scare with Jeremie Frimpong (ankle) before the win over the USA, but the Bayer Leverkusen right-back formed part of a fully-fit squad for that game, and Van Gaal should have everyone available for the quarter-final too.
Inter Milan centre-back Stefan de Vrij could not train on Sunday due to discomfort, but he has since returned to the group to challenge the established order of Jurrien Timber, Virgil van Dijk and Nathan Ake, although he will likely be fighting a losing battle there.
Depay's opener against the USA made it 24 goals in his last 30 outings for the Netherlands - as well as 10 assists - and the Barcelona attacker should once again partner up with Gakpo in an untouched Dutch XI.
As far as Argentina are concerned, Sevilla attacker Papu Gomez came off with a sprained ankle in the 50th minute against Australia and is a doubt for the contest, but Angel Di Maria is stepping up his recovery from a quadriceps problem and should be fit to replace his stricken teammate.
Scaloni has no injury concerns elsewhere and continues to keep faith in the centre-back pairing of Cristian Romero and Nicolas Otamendi, which should remain as it is despite constant pressure from Lisandro Martinez.
The likes of Angel Correa and Leandro Paredes were put through their paces in a training ground XI earlier this week, but neither man will be expected to edge out Di Maria or the impressive Enzo Fernandez for a start in the quarter-final.
Netherlands possible starting lineup:
Noppert; Timber, Van Dijk, Ake; Dumfries, De Jong, De Roon, Blind; Klaassen; Gakpo, Depay
Argentina possible starting lineup:
Martinez; Molina, Romero, Otamendi, Acuna; Fernandez, De Paul, Mac Allister; Di Maria, Messi, Alvarez
We say: Netherlands 2-2 Argentina (a.e.t, Argentina to win on penalties)
The footballing gods should not deliver another drab 0-0 with so much offensive talent on the Lusail field and the Dutch's penchant for lightning-quick counter-attacks, and both sides also possess a slight vulnerability to suggest that a high-scoring affair should be on the menu.