Regular pay rose at an annual rate of 7.7% between July and September, faster than price rises over the same period.
However, official figures showed that wage rises are starting to slow in some industries.
And while the UK's unemployment rate was unchanged at 4.2%, the number of job vacancies has continued to fall.
Between August and October, the estimated number of vacancies in the UK fell by 58,000 to 957,000,the Office for National Statistics (ONS) said.
That was the 16th month in row it had fallen, although the total number of vacancies remains well above pre-pandemic levels.
For nearly two years, prices of goods such as food and energy have been rising much faster than wages, putting pressure on household finances.
Inflation has now started to ease, although consumers are increasingly being squeezed by higher interest rates which have driven up the cost of mortgages and other loans.
The latest figures show that regular pay - which excludes bonuses - rose by 1% in the three months to September after taking inflation into account.
That was the largest increase since the three months to September 2021, the ONS said.
Average weekly earnings were estimated to be Â£621 for regular pay in September, and Â£673 for total pay (which includes bonuses).
While there may be relief for many as the gap between pay rises and inflation widens, it is largely due to slowing price rises rather than big jumps in pay.
Wage growth is actually dwindling in some areas - such as construction and manufacturing - as expectations of future price rises diminish and the jobs market starts to weaken.
Moreover, the average pay rise awarded in September was the smallest for six months, and in the private sector the typical rise was the least generous since January.
The Bank of England has warned that higher interest rates are likely to hit companies' hiring plans next year, driving up unemployment to 5%.
This would result in more than 150,000 job losses and mean that wage growth is likely to slow further.
Jake Finney, an economist at PwC UK, said the latest indications were that the labour market is "gradually cooling, not collapsing".
He said he expected the Bank of England to keep interest rates unchanged at its next meeting in December, as it waits to see the impact of higher interest rates on the labour market and the economy more generally.
Currently, financial markets are not expecting the Bank to push interest rates higher than the current level of 5.25%, and some analysts believe rates could be cut at some point next year.
Against this backdrop the Chancellor, Jeremy Hunt, will reveal how much the National Living Wage will rise by next spring at next week's Autumn Statement.
He has pledged it will be at least Â£11 per hour for the main rate, an increase of over 5%, or Â£1,000 per year for a full-time worker.
While this will be hugely welcome for the two million workers paid this wage, some employers are already fretting about the impact on costs as business feels the squeeze.
Marc Bridgen is the owner of The Dog at Wingham, a gastropub and boutique hotel in Kent. While he supports the forthcoming rise in the National Living Wage, he says he may need to increase his prices to pay for it.
"We've been absorbing [cost rises] for a long time, and we recently had to increase our prices. If we get to April and our cost base goes up by, say, 10% on the wages, it's more than Â£1,000 a week, which is a lot of food and drink to sell."
Responding to the latest labour market figures, the chancellor said: "It's heartening to see inflation falling and real wages growing, keeping more money in people's pockets.
"Building on the labour market reforms in spring, the Autumn Statement will set out my plans to get people back into work and deliver growth for the UK."
Labour's shadow work and pensions secretary, Liz Kendall, said the figures showed "the Tories' failure on the economy".
"Our employment rate still hasn't got back to pre-pandemic levels, unlike every other G7 country, and a record number of people remain locked out of work due to long-term sickness."
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Wages have risen faster than inflation by the most for two years, but there are signs the jobs market is starting to weaken.