Emiliano Martinez was the hero as Argentina edged past the Netherlands in a penalty shoot-out following an absorbing 2-2 draw.
Martinez produced saves from Virgil van Dijk and Steven Berghuis before Lautaro Martinez slotted home the winning spot-kick as Argentina secured a place in the semi-finals against Croatia.
Lionel Messi looked to have won it for Argentina in normal time by creating Nahuel Molina's opening goal before adding another himself from the penalty spot, only for two late Wout Weghorst efforts to send the game beyond 90 minutes.
A low-key first half in which both teams were content to keep possession without being good enough to create anything with it was finally ignited by the brilliance of Messi 10 minutes before the break.
The Paris Saint-Germain star picked the ball up 40 yards from goal, took a couple of players out with a body swerve, and then slid it through to Molina who finished well from 10 yards.
The second goal for Argentina came after 73 minutes following a senseless trip by Denzel Dumfries on Marcos Acuna just inside the edge of the penalty area.
Messi, who missed from the spot against Poland earlier in the tournament, made no mistake this time, powering his effort to Andries Noppert's left.
Netherlands boss Louis van Gaal threw on Weghorst with 12 minutes to go and it proved to be a masterstroke.
Weghorst halved the deficit five minutes after his introduction, heading home Berghuis' inswinging cross, and landed another telling blow with virtually the last kick of normal time.
With everyone in the stadium expecting Teun Koopmeiners to go for goal with a free-kick 20-yards out, he instead slipped a clever ball through to Weghorst and he did the rest, sliding it past Emiliano Martinez.
A match that had seen regular flashpoints in the second half boiled over again after the final whistle with players from both sides embroiled in pushing and shoving.
Argentina pressed for a winner in extra-time but could not find a breakthrough, with Enzo Fernandez coming closest in the final minute with a 20-yard drive then crashed against the outside of the post.
Emiliano Martinez then took centre stage, saving the Netherlands' first two efforts to put Argentina in control. Enzo Fernandez put his effort wide to increase the tension but Lautaro Martinez made no mistake, firing home to spark wild celebrations.
What does it mean? Argentinian joy is unconfined
What a day to be an Argentina fan! News of Brazil's penalty shoot-out defeat to Croatia prompted scenes of delight in the stands at Lusail Stadium before their own team did what their arch-rivals could not and secured a place in the World Cup semi-finals.
Argentina still look functional rather than fluent but if they can continue to keep it tight at the back, they have a genius in Messi to open games up at the other end.
Simply superb. He might not dominate games like he did 10 years ago but he still delivers in the key moments.
He created the first with typical impish brilliance and held his nerve twice to slot away two penalties, including one in the shoot-out.
After 78 minutes of achieving largely nothing in attack, Van Gaal threw on Weghorst in the hope he could deliver some late magic. The Besiktas striker delivered in spades.
A trademark glancing header was to be largely expected but his second goal certainly wasn't, a smart finish after a clever free-kick routine that caught out the Argentina defence.
Argentina go forward to meet Croatia in Tuesday's first semi-final while the Netherlands head home.