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.
But although lower than its expectations, inflation is still twice the Bank of England's target rate, and has now been one percentage point or more above target for 16 months.
This has led to calls for the Bank to raise interest rates - the policy tool used to combat rising prices.
"There is little cause for celebration as the inflation rate remains well above average and continues to exert significant pressure on household disposable income and discretionary spend," said Neil Saunders, consulting director at research group Verdict.
Last week, the Bank's Monetary Policy Committee (MPC) kept rates at a record low of 0.5% for the 25th month in a row.
Next week it will reveal how members voted.
Three of the MPC members called for a rise in rates at last month's meeting.
They and some other economists have argued that rates must rise in order to combat rising prices, which are eroding consumers' spending power.
Those members that voted for rates to be held, backed by a number of leading economists and business groups, argue that a rise in rates could jeopardise the UK's fragile economic recovery, particularly in light of the economy's 0.5% contraction in the final three months of last year.
They say that inflation is high due to temporary and external factors, such as the recent rise in VAT and high commodity prices, and has yet to be reflected in wage increases, which would provide longer-term upward pressure on prices.
The rise in VAT came into effect in January, and so will fall out of the inflation calculations at the beginning of next year.
They insist, therefore, that, given time, inflation will fall away of its own accord, without the need to raise rates in the short term.
The latest ONS figures could strengthen their resolve to keep rates on hold for longer.
"The prospect of a May rate hike has been significantly reduced by today's surprise drop in UK CPI," said James Knightley at ING.
He added that record falls in High Street sales in March, reported by the BRC on Tuesday, could also help to sway opinion on the committee towards holding rates again.