It was a tight race, in which the Brits briefly had their noses in front before New Zealand came home impressively. They started with a 1min 03s first kilometre, followed by splits of 56, 567 and 57s to smash the national record by more than a second.
"It's unbelievable how well they went," Carswell said. "They outdid themselves in riding the last couple of days. I couldn't be happier."
The quartet of Kennett, Bulling, Ryan and Frame recorded 3:56.198 in winning their semifinal against Switzerland. Britain saw off the Germans in the other semi. Australia won bronze, overlapping Germany.
The pursuiters weren't flavour of the month at the Commonwealth Games programme in Glasgow last year. It was felt they hadn't been as impressive as expected, on their way to a bronze medal. There's a different tune now.
"It's brilliant," Carswell said of the impact for the Cycling New Zealand programme.
"They're really young, they're going to get stronger over the next year and a half leading into Rio. We are very lucky with the strength of our programme at the moment. It's pretty exciting."
Frame is just two years off road riding, while Kennett was well back in the pecking order at Christmas, having battled to get regain form after Glasgow.
Carswell also introduced new tactics, with each rider doing stints of a lap and a half, rather than one lap, which demanded plenty of strength.
The win took New Zealand to three medals at the champs, following the silver for the men's team sprint 24 hours earlier, and Eddie Dawkins' silver in the keirin final.
Dawkins looked impressive throughout the keirin, winning his semifinal with a powerful burst. He stayed on the inside behind the leader in the final and although he found an opening around the final bend, ran out of track to catch flying Frenchman Francois Pervis.
Dawkins' sprint teammate Sam Webster finished sixth in the final.
"I'm over the moon," Southlander Dawkins said. "It's only the second time I've been in the final of the keirin but the first time I've been competitive."
Having been part of the sprint team the previous day, Dawkins admitted he was still grumpy before the keirin.
"But this has made up for that result yesterday. Scars do heal but they still leave a mark.
"There is definitely unfinished business for that team sprint next year and on to Rio [Olympic Games]."
The women's 4000m team pursuit quartet of Rushlee Buchanan, Lauren Ellis, Jaime Nielsen and Georgia Williams finished fourth.
They were beaten by eventual winners Australia - in a world record time - in their semifinal, then losing the bronze rideoff to Canada by just under five seconds.
