Britain, who came sixth in Beijing and failed to qualify for Athens, showed fighting spirit throughout the tournament, not least taking in their stride when their captain Kate Walsh broke her jaw in the team's first match.
Walsh came back to play six days later, having had a titanium plate inserted during surgery, but could not save her side from a semi-final defeat to world champions Argentina two days ago.
Britain seemed to have digested that setback better than New Zealand, who lost to the Netherlands in the first Olympic penalty shootout, and Kiwi skipper Kayla Sharland said some players had not taken this bronze medal match seriously enough.
"People have to question whether they prepared well for this game in terms of their individual preparation and I question that in some people," Sharland said.
"It's disappointing and to let yourselves down on the final hurdle is, I think, the most frustrating part."
The Kiwis were pre-tournament outsiders, having finished Beijing four years ago without winning a game, but knocked out more prestigious sides in the group stage, such as Germany.
Britain controlled the game but had few chances from open play and could not convert two penalty corners in the first half, giving New Zealand the chance to build up pressure towards the interval.
The Kiwis upped the pressure in the second half and could have found a way back in, when Katie Glynn deflected a pass from Cathryn Finlayson struck the post in the first minute.
But Britain pushed to force New Zealand into errors in the D to take advantage of their strong penalty corners. Their tactics paid off.
In the 45th minute, the hosts scored from a penalty corner when Alex Danson deflected a pass from Walsh for her fifth goal in London.
Crista Cullen scored from a well-placed drag flick penalty corner in the 59th minute - also her fifth - and Sarah Thomas deflected another corner into the goal four minutes later.
The Kiwis, whose previous best Olympic placing was sixth, pulled back a goal with a penalty corner deflection with just two minutes left.
"I'm absolutely blown away. I am so proud to be a part of this team. We gave everything. Two days ago bronze became our gold and we promised each other we would not go away with anything less," said Danson, who added she would celebrate with a packet of sweets as she had given them up in January.
Prince William's wife Kate, the Duchess of Cambridge, who has been a frequent spectator at the hockey tournament, went to congratulate the British side in the changing rooms, and coach Danny Kerry said his team had then spent "half an hour discussing her clothes".
"I've lost my voice in the last 10 minutes shouting and celebrating it. This means everything," said Britain's Ashleigh Ball.
"This is what it's all about. To put in a performance when it mattered and come away with bronze, we're just over the moon."