The Office for National Statistics said services output grew by 0.2% between November and December 2015, with output for November being revised up from 0.2% to 0.3%.
The ONS confirmed that the wider economy grew by 0.5% during the fourth quarter of 2015 in its second estimate of gross domestic product (GDP).
A robust performance in the services sector offset a tough end to 2015 for the construction and production sectors.
Production, including manufacturing, contracted by 0.5% in the fourth quarter, while construction output fell by 0.4%.
The GDP figure for the fourth quarter came as a relief amid heightened market volatility on global growth fears, with some economists having pencilled in GDP to fall to 0.4% between October and December.
It means GDP grew at the same level as previously estimated for the whole of 2015 at 2.2%, down from the nine-year high of 2.9% the year before.
Chancellor George Osborne warned last month that the UK was facing a dangerous cocktail of risks in 2016, pointing to falling oil prices, slowing growth in China and turbulence in the markets.
A spokesman for the Treasury said: "These figures confirm that Britain continued to see steady growth at the end of last year.
"But following recent downgrades to the global economic outlook it's vital that we don't stop working through our plan that's building resilience and providing an anchor of stability in uncertain times."
The dominant services sector - which accounts for three-quarters of the UK economy - was buoyed by a strong performance in December, with the index of services increasing 2.1% compared with the same month in 2014.
But the ONS revealed more grim news on Britain's trade deficit, which widened to £16.6bn in the fourth quarter from £14.7bn the quarter before.
It said business investment fell 2.1% in the fourth quarter to £43.1bn compared with the quarter before.
Chris Williamson, chief economist at Markit, said the ONS's economic update paints "a picture of an unbalanced economy that is once again reliant on consumer spending to drive growth as business shows increased signs of risk aversion".
He added: "Growth is being supported by firms increasing the wages paid to workers alongside low inflation, which is clearly good for household incomes in the short term.
"But for a sustainable recovery, which involves improvements in productivity and profits, we also need to see business investment revive, something which will only happen when business confidence lifts higher again."
Howard Archer, chief European and UK economist at IHS Economics, now expects GDP to grow 2.1% for 2016.
He said: "The UK's expansion is currently being pressurised by heightened global growth concerns and financial market volatility, while there is mounting domestic uncertainty as the referendum on UK membership of the European Union looms."