Goalkeeper Emilio Martinez was the shootout hero after another inspirational Lionel Messi performance led Argentina into the World Cup semi-finals.
The Argentines beat the Dutch 4-3 on penalties after squandering a two-goal lead at the death.
Martinez saved the first two Dutch penalties from captain Virgil van Dijk and Steven Berghuis, and Lautaro Martinez clinched matters after teammate Enzo Fernandez had been denied by the post in the final minute of extra time with the score locked at 2-2.
Messi fed Nahuel Molina with a sensational pass to score in the 35th, and then calmly converted a 73th-minute penalty as Argentina seemed well on course with a 2-0 lead.
But substitute Wout Weghorst headed the Dutch back into the game in the 83rd and then forced extra time 11 minutes into stoppage time in an extraordinary free-kick trick play.
Messi tied Gabriel Batistuta on an Argentinian record 10 goals at the World Cup and can gain sole possession of the record in the semi-final and the final or third-place game as he aims to win the biggest prize in football in his fifth and final World Cup appearance.
Messi will claim the overall World Cup match record if he plays in the remaining two games. He played his 24th match on Friday, with record holder Lothar Matthäus of Germany one ahead on 25 matches.
The Copa America champions next meet Croatia on Tuesday after the 2018 runners-up shocked record five-time winners Brazil 4-2 on penalties after a 1-1 deadlock in 120 minutes.
The Dutch failed to reach the last four for the third time in four editions and suffered a shootout loss to Argentina just as in the 2014 semi-finals.