UK unemployment fell by 115,000 between July and September to 1.96 million, according to the Office for National Statistics (ONS).
It was the 18th consecutive fall in the total, the ONS said.
Figures also showed that one measure of average earnings growth beat inflation for the first time in five years.
The ONS said earnings excluding bonuses rose by 1.3% in the year to September, ahead of the 1.2% Consumer Prices Index inflation rate.
Including bonuses, earnings rose by 1%.
Pay has lagged inflation since the global financial crisis, but in recent months earnings have been rising just as the pace of price growth slows.
The number of people claiming Jobseeker’s Allowance was 931,700 in October, 20,400 down on September, and the 24th consecutive monthly cut.
The ONS said employment rose by 112,000 in the latest quarter to 30.7 million, the highest since records began in 1971.
Around 14.7% of workers, or 4.5 million, are self-employed, down by 88,000 on the quarter but up by 279,000 on a year ago, while the number of part-time workers wanting a full-time job remained at about 1.3 million.
Employment Minister Esther McVey said: “Record numbers of people in work means more people with the security of a regular wage who are better able to support themselves and their families.
“With the vast majority of the rise in employment over the last year being full-time, it’s clear that thanks to the government’s long-term economic plan, we are helping businesses to create the jobs that people need.”
But Stephen Timms, the shadow employment minister, said there was “no room for complacency”. He told the BBC: “Youth and long-term unemployment remain a serious problem, so there is a lot more do.”
And Paul Kenny, general secretary of the GMB union, said: “Many of the new jobs are precarious and badly paid while the real value of take-home pay for the rest of the workforce is 13% below pre-recession levels.”
On pay growth, IHS Global Insight’s chief UK economist, Howard Archer, said the news would be a relief for consumers.
But he added: “This is still really more to do with low inflation than markedly improving earnings. However, earnings growth did take a much-needed decent step in the right direction in September.”