Andy Hayward became the first New Zealander to score a hat-trick at a World Cup in eight years as the Black Sticks snuck home 5-4 on penalties against South Africa to finish ninth – for the third time (1986, 2002).
The African champions' were ahead 1-0 at half-time and then held a 4-3 advantage after five goals were scored in less than 10 minutes in the second spell.
But Hayward's three second-half goals proved crucial as he saved the Black Sticks' blushes with a drag-flick after the final hooter to level the high scoring affair, played beneath blistering afternoon sun in New Delhi, at four goals apiece.
Two sudden-death extra-time periods saw both sides suffer from fatigue, therefore, adopt a cautious approach and the match was sent to penalties.
There, New Zealand's goalkeeper Kyle Pontifex snuffed two attempted shots and stand-in captain Dean Couzins slotted one past Erasmus Pieterse for victory.
But New Zealand coach Shane McLeod was far from impressed, despite his side's likely one place rise - to seventh - in the world rankings after Pakistan's disastrous showing.
"Some players did not perform and we have standards which fell well short today," McLeod said.
"As much as I don't like to admit it there was a hint of complacency among our players and it showed."
Losing regular captain Phil Burrows to a calf-strain in the second-round loss to the Netherlands as well as key striker Simon Child's decision not to attend because of security fears, had hurt the New Zealand side.
This meant 19-year-old Nick Wilson had to play as the senior striker.
Australia plays Germany in the World Cup final on Saturday.
McLeod was prepared to make the 'hard calls' in naming his 18-man squad next week for a four-nation tournament in Nottingham in July.
"We will freshen our squad now. It would be a crime if we didn't introduce new players," McLeod said.
The Black Sticks will use the four-nation tournament as build up for the Champions Trophy, which includes the top five teams in the world, plus New Zealand, in Monchengladbach, Germany from July to August.