The UK Consumer Prices Index (CPI) annual rate of inflation has fallen to 4%, down from 4.4% in February.
The drop was largely due to a record monthly fall in the price of food and non-alcoholic drinks, which fell 1.4%, compared with a rise last year.
Retail Prices Index (RPI) inflation - which includes mortgage interest payments - fell to 5.3% from 5.5% in February.
The fall eases pressure on the Bank of England to raise interest rates.
CPI is now back to the level recorded in January.
The pound fell almost 1.5 cents against the dollar immediately after the figures were announced, to $1.6238, as investors decided the Bank was unlikely to raise rates as soon as they had previously thought.
Against the euro, it fell one cent to 1.1237 euros.
The Office for National Statistics (ONS) said supermarkets had reduced their prices in March.
The British Retail Consortium (BRC) said increased competition at a time when consumers were spending less meant margins were being squeezed.
A record 40% of supermarket sales were now discounted or part of a promotional offer, it added.
Fruit prices fell by 4.7%, while bread and cereals dropped by a record 2.6% when compared with March last year, the ONS said.
Falls in the price of air flights, games and toys also helped to offset rises in energy costs and cars, it added.
However, analysts warned that the rate of inflation could begin to speed up again in the coming months.
The Bank itself expects the inflation rate to pick up for the remainder of this year, potentially rising as high as 5%, before falling back to its target rate of 2% by the end of next year.
Economists had expected the CPI rate to stay at 4.4% in March, or perhaps even rise slightly.
"It's not only a surprise, it's a very welcome surprise," said Philip Shaw at Investec.