The 11 per cent fall reflects average petrol prices over the quarter. Statistics NZ said that by the end of the quarter prices at the pump were 1.8 per cent higher than the quarterly average.
Economists were struck, however, by how widespread the weakness in inflation pressures is.
The Reserve Bank's preferred measure of core inflation came in at 1.3 per cent, unchanged from December's record low for the series.
Another measure of core inflation, the 10 per cent trimmed mean, which disregards the largest price rises and falls and looks at the 90 per cent of the CPI in between, was just 0.6 per cent higher on an annual basis.
And of the nearly 700 items in the CPI, 43 per cent - representing just over a third by expenditure weight - fell in price in the March quarter.
"Low annual inflation in the services sector - at 1.4 per cent year on year the lowest since September 2012 - is also an indication that wage pressures remain contained," said ANZ economist Mark Smith.
Construction costs inflation (the price of newly built houses excluding land) in Auckland was 0.7 per cent for the quarter and 5.9 per cent for the year, while nationwide the increases were 0.7 and 5 per cent.
Auckland rents rose 2.6 per cent for the year, marginally stronger than the 2.3 per cent recorded nationwide and suggesting that rental yields do not explain the city's rampant house price inflation.
Westpac economist Michael Gordon said that if there was a note of caution to be struck from the March figures, it was that non-tradeables inflation was stronger than expected - 2.3 per cent versus the Reserve Bank's forecast of 2.1 per cent.
"However, it seems that any substantial price increases are occurring in increasingly isolated pockets, there's certainly no sense that the strong economy is translating through into generalised inflation," Gordon said.
Bank of New Zealand economist Craig Ebert expects the annual inflation rate to pick up marginally to 0.3 per cent in June and September.
"But from there we see it as all onwards and upwards for annual CPI inflation, with it picking up to 2.3 per cent by the September 2016 quarter - that relies on the exchange rate moderating from its present heights."
ASB economists also believe the March 2015 quarter will mark the low for inflation in this cycle, forecasting it to pick up to back over 1 per cent by the end of the year, though that also assumes the US dollar will continue to strengthen.
"Meanwhile, non-tradeable inflation is likely to continue to push higher," said ASB chief economist Nick Tuffley.
"Housing-related inflation will continue to accelerate as housing shortages become more acute in Auckland and competition for construction resources between Auckland and Canterbury escalates. Steady economic growth will continue to reduce the spare capacity that remains in the economy and feed through to stronger domestic inflation pressures outside of housing."
On the up, just
• 0.1% annual inflation rate - lowest since 1999.
• 11% fall in petrol prices the main downward contributor.
• Excluding petrol the rate would have been just 1%.
• 5% construction costs inflation for the year.
