The Government said that unemployment was moving in the "right direction" despite an increase in the number of people on Jobseeker's Allowance and a youth jobless total of almost a million.
Unemployment fell by 17,000 in the quarter to February, to 2.48 million, a rate of 7.8%, down by 0.1% on the quarter.
The so-called claimant count increased by 700 last month to 1.45 million, including 462,300 women, the highest figure since October 1996.
The number of jobless 16 to 24-year-olds increased by 12,000 over the quarter to 963,000, while the total for 16 and 17-year-olds increased by 14,000 to 218,000, the highest since records began in 1992.
The number of unemployed 18 to 24-year-olds fell by 2,000 on the quarter to reach 745,000.
Today's data from the Office for National Statistics (ONS) showed that the number of unemployed men fell by 31,000 to 1.45 million and increased by 14,000 for women to just over a million.
Changes to benefit rules have seen women switching from income support to Jobseeker's Allowance (JSA) over the past two months.
The number of female claimants has now increased for nine months in a row and fallen for men for 14 consecutive months.
Employment has increased, showing a 143,000 rise to 29.23 million, although the figure is still 331,000 below the pre-recession peak reached in May 2008.
The latest increase was driven by full-time employment which rose by 140,000, the biggest rise in this group for four years.
The number of people classed as economically inactive fell by 71,000 to 9.3 million following a 48,000 reduction in those listed as having a long-term illness.
Employment Minister Chris Grayling said: "These figures are another step in the right direction.
"It's good news to see a rise in the number of full-time jobs in the private sector and the fall in unemployment is welcome.
"It is also reassuring to see a fall in the number of young people not in full-time education who are unemployed.
"However, there are challenges ahead and our priority is to continue to support the economy, by reducing the deficit and putting in place measures to encourage growth in the private sector."
The Government said tackling youth unemployment remained a priority, centred on growth in apprenticeships and work experience places.
Unison general secretary Dave Prentis said: "The damage caused by the Government's savage cuts-driven policies is clear, with young people and women being hit the hardest.
"We face a lost generation of young people being priced out of education and with the prospect of job opportunities in the future fading fast."
John Walker, chairman of the Federation of Small Businesses, said: "It is extremely worrying that nearly one million of our school leavers and graduates are unemployed. Our research shows that only one in 10 small firms took on an apprentice or a graduate intern over the past year.
"Businesses need incentives to tackle youth unemployment. The Government must extend the National Insurance contributions holiday to existing firms. This would help them to employ."
TUC general secretary Brendan Barber said: "Today's figures are a welcome relief for those looking for work but our labour market recovery is still far from secure.
"The surprise fall in unemployment is good news for the millions of people looking for work, although the fall in the number of vacancies from last month is a worrying sign.
"The news for those in work is less positive, with earnings growth falling and the gap between wages and inflation rising sharply to 3.5%. The growing earnings gap is piling the pressure on people's living standards.
"Rising long-term unemployment and youth joblessness close to a million offer a sobering reality check on today's upbeat figures."
Martina Milburn, chief executive for youth charity The Prince's Trust, said: "Unemployed young people living in the UK outnumber all the runners who have ever taken part in the London marathon since it launched 30 years ago.
"With the total number of unemployed school leavers at its highest since records began, the prospects for a generation of young people are looking increasingly bleak."
Dr John Philpott, chief economic adviser at the Chartered Institute of Personnel and Development, said: "While the jobs figures are apparently signalling green for go, they reflect an improvement in the labour market at the turn of the year and don't tell us anything much about the road ahead.
"Indeed, the most up to date figures for vacancies and claimants of Jobseeker's Allowance suggest that labour market conditions softened again in the early spring and it remains likely that unemployment will start to rise again later this year.
"Especially welcome in today's figures is a substantial rise in the number of people working full-time, although this was still insufficient to prevent a further increase in the number of people working part-time who would prefer a full-time job."