In a thrilling race, the Kiwis started strong and took charge from the second 500m, holding off the Germans and Brits at the end.
It was a historic win for Hamish Bond, who collects his third Olympic gold medal - the first New Zealander to win a gold medal at three successive Games.
Bond also won gold in London and Rio with Eric Murray in the coxless pairs.
With three, he sits one behind Ian Ferguson's record tally of four and alongside the legendary Peter Snell and Paul MacDonald.
The team is made up of Tom Mackintosh, Bond, Tom Murray, Michael Brake, Dan Williamson, Phillip Wilson, Shaun Kirkham, Matt Macdonald and coxswain Sam Bosworth.