Stats NZ said transport prices rose 3.9 per cent, the biggest quarterly rise in over a decade.
Petrol prices rose 7.2 per cent, the biggest quarterly rise since June 2015.
Despite this, petrol prices are 3.8 per cent lower than they were a year ago, the department said.
"Global oil prices plunged in early 2020 as the Covid-19 pandemic took hold. Prices have risen since then," prices senior manager Aaron Beck said in a statement.
The weighted average price of a litre of 91 octane was $2.00 in the March 2021 quarter, up from $1.87 in the December 2020 quarter and down from $2.09 in the March 2020 quarter.
By the end of the quarter, petrol prices were about 3.3 per cent higher than the average over the quarter.
Rent prices rose 1.0 per cent, the biggest quarterly increase in a year.
Annual rent prices increased 2.7 per cent.
The price of building a new home increased 3.5 per cent in the year to March 2021, the biggest annual increase since June 2019.
However, this is less than half of what it was when it peaked at almost 9 per cent in 2004.
Annual inflation for the year to March 2021 was 1.5 per cent, slightly higher than the 1.4 per cent increase in the year to December 2020.
Removing petrol, annual inflation was 1.7 per cent, down from 2.1 per cent in the year to December.
If food, household energy, and vehicle fuels were removed, annual inflation was 2.0 per cent, down slightly from 2.1 per cent in the year to December, the department said.
The New Zealand dollar was unchanged following the data, trading at US71.72c.
