The first half of the long and fiery match proved to be a tight affair with plenty of tension on the pitch and the sidelines.
After an evenly poised start to the match it took a bit of magic from Lionel Messi to unlock the game, with the Argentina playmaker threading a perfectly placed pass in between the Dutch defense for Nahuel Molina to run on to.
Reuters reports the full-back took one well-controlled touch to take it into the box before coolly placing his shot past the Netherlands keeper to score the opening goal in the 35th minute.
The game remained without another goal up until the 73rd minute, when Argentina was awarded a penalty after Denzel Dumfries brought down Matias Acuna with a light kick to the ankle just inside the box.
Lionel Messi stepped up to take the spot-kick and curled his shot to the right hand side of Noppert to score his fourth goal of the tournament.
Argentina continued to dominate possession for large spells of the second-half and the Dutch found no luck in attack.
However, Dutch big man Wout Weghorst gave the Oranje a glimmer of hope in the 83rd minute, getting on the end of a long cross to send a glancing header bouncing to the left of the Argentina keeper.
With the deficit now cut to just one-goal, the Dutch side switched up a gear and went on the offensive, bombarding the Argentinian defence.
Tensions between both sides began to boil over as the game came down to the final moments, with the Dutch squad rushing onfield to barge over Argentina midfielder Leandro Paredes after he provocatively cannoned the ball at their bench.
In the final minute of the match, the Netherlands won a free kick just metres from the edge of the box with only thirty seconds left to go.
As the Dutch side sat on the edge of elimination, Teun Koopmeiners stepped up to take the free kick and surprised everyone with a cheekily rolled a pass under the jumping wall.
The ball fell straight to Wout Weghorst who took a touch before slotting it past Martinez to score the equaliser and send the Netherlands fans into hysterics.
As the match entered an additional thirty minutes of extra-time, tempers frayed on both sides with 11 yellow cards handed out in regulation time.
The first-half of extra-time proved to be tense but uneventful, with only a handful of half chances coming Argentina's way.
The second-half followed suit but heated up in the final five minutes as Argentina came close to scoring on several occasions, the closest coming as Enzo Fernandez smashed a shot off the left-hand post in the final minutes.
As the match came down to a penalty shootout, it was Netherlands captain Virgil Van Dijk who stepped up to take the first attempt.
The defender struck a powerful shot to the right hand side of Emiliano Martinez but the Argentina keeper guessed correctly and saved the shot brilliantly.
Lionel Messi non-chalantly scored Argentina's first spot-kick, rolling it low and slow to the other side of Andries Noppert in goal.
Next up, Steven Berghuis took the same route as Van Dijk but this time to the other side, however, Martinez once again produced an acrobatic save to dash Dutch hopes.
Leandro Paredes converted Argentina's second penalty with a well-placed shot right into the corner, giving Noppert no chance.
Teun Koopmeiners changed the course for the Netherlands, scoring his penalty with a cool finish. Argentina's Gonzalo Montiel quickly responded with a successful penalty of his own to make it 3-1 to Argentina with two players left to take.
Goalscorer Wout Weghorst stepped up for his country's fourth penalty and calmly sent Martinez the wrong way before Enzo Fernandez dragged his shot wide to the left, closing the gap to 3-2.
Luuk De Jong scored the Netherland's final penalty, once again sending Martinez to the wrong side to level the scores.
The responsibility of the final penalty fell to Lautaro Martinez, who with the weight of a nation on his shoulders smashed the ball into the top right corner to win the game and send Argentina to the semi-finals.
Argentina will face Croatia in the semifinals after the Balkan nation also narrowly beat Brazil on penalties in their quarterfinal earlier this morning.
Argentina's Lionel Messi on the ball in the first half of FIFA World Cup quarter-final against Netherlands. Photo: AFP