The TNS BMRB survey showed the No campaign leading by 14%, a figure that is down from 19% in September. Conducted between December 3 and December 10, the latest poll confirmed a gradual shift in support towards the pro-independence efforts led by First Minister Alex Salmond over the past three months.
Yes Scotland said they were "on the right trajectory" following the findings while the pro-UK Better Together insisted they had retained a "strong lead".
The TNS BRMB poll of 1000 people aged over 16 showed support for independence now stands at 27%, up from 26% in November and 25% in September.
By contrast, support for Scotland staying in the UK has slipped from 44% in September to 42% in November and 41% now.
The number of don't-knows rose by a single percentage point to 33% compared with last month.
Among those certain to vote, the No campaign's lead was 15 percentage points - 45% to 30% - according the latest poll.
The lead among definite voters has fallen from 22 points in September when 50% of those certain to vote backed staying in the UK, compared with 28% supporting independence.
The poll came as Fitch, which monitors and regularly reports its view on the creditworthiness of nations, last night entered the fray, warning: "The monetary arrangement following Scottish independence could become a source of uncertainty even if Scotland remained in the sterling currency zone.
"As the intensification of the eurozone crisis showed in 2012, a monetary union without fiscal and banking union is unstable and the prospect of an exit could lead to high volatility and market turbulence, potentially detrimental to all members."
The Treasury seized on the remarks, with a spokesman saying: "The UK Government has repeatedly said a currency union is highly unlikely to be agreed as it is highly unlikely to be in the interests of either Scotland or the UK. Fitch make this same point; yet another example of why the Scottish Government needs a plan B."
Alistair Darling, leader of the pro-UK Better Together campaign, described the Fitch report as "another blow to Salmond's credibility on the central issue of what currency Scotland would use after leaving the UK".
The former Labour Chancellor added: "It is increasingly obvious that the idea of a currency union is dead in the water. To be successful, a currency union requires fiscal and political union; the very thing the SNP are campaigning to dismantle in the United Kingdom."
He added: "This will only increase the pressure on Alex Salmond to tell us what currency we would use if the rest of the UK refuse a currency union. What is the plan B?"
But a Scottish Government source played down the warning, saying: "Comparisons with the eurozone are wrong because the Scottish and rest of the UK economies are well-matched with almost identical levels of productivity, unlike the disparate economies of the euro area."
He pointed out a shared currency within a common sterling area had been backed by the expert work of the Fiscal Commission, by many leading business figures, and by Deutsche Bank and Citigroup.
"Sharing the pound will also be in the overwhelming interests of the rest of the UK and has been described by No campaign leader Alistair Darling as 'logical' and 'desirable'," he added.
Commenting on the poll, Tom Costley of TNS in Scotland said: "The narrowing of the gap represents a drift in both the Yes and the No votes rather than any strong movement on either side.
"It underlines the importance for both Yes and No campaigners of engaging with the one third of the electorate who remain undecided."
A Yes Scotland spokesman described the poll as encouraging, saying: "This data confirms our own research which clearly shows that the more people learn about the benefits of independence, the more likely they are to vote Yes."
Better Together campaign director Blair McDougall stressed how the SNP Government had spent hundreds of thousands of pounds of taxpayers' money promoting its White Paper but four subsequent polls had shown it had made "little impact".
Scottish Secretary Alistair Carmichael said: "We are winning the arguments because the way in which we have approached it has been more substantial and much more restrained."