The win gives the Dutch their first shot at gold in 20 years, having been relegated to bronze in three of the last four Games. They now play China or Germany for the top podium spot.
"You can see how happy we are. It's great finally to be in the finals and to know we're sure of a medal," said midfielder Ageeth Boomgaardt.
The semi-final started nervously with both teams attacking hesitantly. Argentina settled down first and won a stunning goal from Agustina Garcia who received the ball with her back to goal, spun around and reverse hit it in.
After a tough half-time talk from coach Marc Lammers, the Dutch came out looking more like the dominant team who have not dropped a game so far in Athens.
"In the first half we were a bit chicken but Marc said 'Just do what you normally do' and we scored twice," said captain Mijntje Donners, who scored one of the goals off a penalty.
The other came from Sylvia Karres who intercepted a cross right in front of goal.
Captain Magdalena Aicega drew Argentina level at 2-2 three minutes from time but try as they might, neither team could net a golden goal in the 15 minutes of extra time and it was onto the penalty shootout.
This time it was sweet revenge for the Dutch who lost the 2002 World Cup to Argentina on penalties.
The huge crowd of orange-clad supporters went wild as each Dutch striker hit the net and two Argentines missed.
"It was their turn tonight," Argentine coach Sergio Vigil said. "If our team hadn't had spirit or had given up fighting, it would be a different matter, but I'm proud of my team."