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The increase is much more than economists had expected.
Excluding quarters impacted by increases to GST rates, the September quarter movement was the highest since the June 1987 quarter, which saw a 3.3% rise, StatsNZ said.
Annual inflation was 4.9% in the September 2021 quarter when compared with the September 2020 quarter.
This was the biggest annual movement since inflation reached 5.3% between the (GST effected) June 2010 and June 2011 quarters.
The September spike was up from a 1.3% increase in the June quarter (3.3 per cent year on year).
Economists had been expecting the Consumer Price Index to land between 1.5 and 1.8% for the September quarter for an annual figure of around 4.4%.
The main drivers were housing-related costs, such as construction of new houses and local authority rates, StatsNZ said.
Prices for construction of new houses were up 4.5% for the quarter, and 12% for the year.
"Both supply-chain challenges and high demand are pushing up the cost of building houses," consumer prices manager Aaron Beck said.
"Construction firms reported that it is hard to get many materials needed to build a house, and that there are higher labour and administration costs."
Wages in the construction industry, as measured by the labour cost index previously increased 3.1% in the year to the June 2021 quarter (the most recent quarter available).
This was due to high demand for labour in the construction industry in the last year.
But quarterly price rises were widespread, with 10 of the 11 main groups in the CPI basket (such as food and transport) increasing in the September 2021 quarter compared with the June 2021 quarter.
Last week, data showed that food prices rose 0.5% in September 2021 compared with August 2021.
It was the sixth consecutive monthly increase.
While the Reserve Bank is expected to continue raising interest rates, economists believe it will remain cautious while New Zealand adjusts to living with Covid-19.
Most expect at least three further increases in the coming months.
The central bank lifted the official cash rate on October 6 - the first time in seven years - by a quarter of a percentage point to 0.5%.