By comparison, Australia's unemployment rate currently sits at 6.9 per cent. New Zealand's unemployment figures also compare favourably to those in the United States, Canada and against the OECD average.
There were 22,000 fewer employed people this quarter than in the June 2020 quarter, Stats NZ said.
Over the September 2020 quarter, unemployment rates for men and women increased by similar amounts, with the women's rate up to 5.8 per cent and the men's rate up to 4.8 per cent.
The underutilisation rate rose to 13.2 per cent. And hours worked nearly bounced back from record falls during lockdown.
"Labour market conditions have deteriorated and are expected to continue to do so, but government support and our relative Covid success have been effective in limiting the damage so far," said ASB senior economist Mike Jones.
"We consider this quarter's unemployment rate to be a roughly 'fair' reading on NZ labour market slack."
While today's data provides a cleaner read than the second quarter - which included the first lockdown - it may still have been affected by pandemic anomalies.
Unemployment actually fell to 4 per cent in the second (June) quarter.
"Only those who are actively looking for work are classified as unemployed, but lockdown conditions made this impractical," said Westpac senior economist Michael Gordon.
But after Stats NZ included some additional questioning in June about whether people were not looking for work for Covid-related reasons, the "true" unemployment rate appears to have been more like 4.6 per cent in the second quarter, he said.
"This quarter, Auckland spent seven weeks in higher Covid-19 alert levels than the rest of New Zealand, with the number of people in employment particularly affected, compared with the rest of the country," said Stats NZ labour market and household statistics senior manager Sean Broughton.
In Auckland, the unadjusted number of employed people fell by 18,000 over the September 2020 quarter, to reach 893,200.
The number of people employed in the retail trade, accommodation, and food services industries in Auckland fell by 8700 to 125,700, a fall of 6.5 per cent.
The number of employed women fell 14,000 to 1,266,000, while the number of employed men fell 8000 to 1,444,000.
The employment rate for women was 61.2 per cent and 71.8 per cent for men.
"Most of the job losses were women," said KiwiBank chief economist Jarrod Kerr.
"Women are bearing the brunt of the burden, as there are more women in the hardest hit tourism industries. And what's more worrying is the growing number of women leaving the workforce. The number of Maori women employed in tourism sectors fell a whopping 20 per cent in the quarter."
Finance Minister Grant Robertson said the data showed the Government's decision to focus the Covid-19 recovery and rebuild plan on jobs was working.
"This is still a difficult time for many New Zealanders, and we are working hard alongside them to create new work and training opportunities," he said.
"We recognise that today's employment statistics show that the economic impact of Covid-19 is falling disproportionately on women, Maori and Pacific peoples. I will be working closely with the ministers in these areas to make sure there is an inclusive recovery and rebuild."
