A great scream of excitement went up when Lisa Walton tapped the last cross of the match into the goal and the players jumped on each other in scenes of jubilation worthy of a final.
The Kiwis now play Australia for fifth and sixth place while South Korea and Japan face off for seventh and eighth.
"To be in the top six in the world is a huge achievement. Most experts said we'd be tenth," grinned coach Ian Rutledge, who ran onto the pitch bouncing one of his players up and down in his arms when the goal went in.
New Zealand, who came to Athens ranked ninth in the world, filled the last place in the six-team Champions Trophy which will be played in Argentina in November.
"The team has changed so much since we were last in the Champions in 2002. We've only been together for about 12 months so it's a great accolade," Rutledge said.
In the other playoff, Japan went down 3-1 to Australia, who failed to make the semi-finals and so lost the opportunity to battle for their third gold in a row.
Australia meet New Zealand on Thursday.