Ipsos MORI has recorded support for a Yes vote up from 30% to 34% since October, while backing for a No vote has gone down three points to 55%.
That is still a 21-point lead for those backing the Union, but a significant narrowing of the gap from 28 points in October.
One source in the Yes camp said: "This is only one poll, so we are not getting carried away. However, it underlines a trend that might indicate the tide is beginning to turn in our favour and it is certainly in line with the feedback we are receiving from our supporters and volunteers on the ground."
A significant finding in the poll for The Times was a surge in support for independence among those aged under 25. The survey did not include those aged 16 to 17, but among those aged 18 to 25 the number backing independence has risen from 27% to 58% since October. Even within the Yes camp there was some scepticism about the credibility of this figure, but overall there was a bullish confidence the trend is now moving their way.
Yes Scotland chief executive Blair Jenkins said: "With the referendum question now agreed, coupled with the full impact of the Westminster Government's welfare cuts becoming more apparent on a daily basis, we are confident people will choose the more positive, optimistic and fairer path that a Yes vote offers."
Better Together leader Alistair Darling said: "Being ahead in the polls is always better than being behind. However, there is no doubt the only poll that matters, and the poll we are absolutely focused on, is the one that will be taking place in autumn next year. We will do everything we can between now and then to win the arguments and win the votes of people in every part of Scotland."
A total of 1003 people in Scotland were polled, with Deputy First Minister Nicola Sturgeon getting a higher approval rating than Mr Darling.
Ms Sturgeon, who is spearheading the campaign for independence, had a net approval rating of +17, with 50% of those surveyed satisfied with her performance compared to 33% who were dissatisfied.
Meanwhile, 33% of people said they were satisfied with the job former chancellor Mr Darling is doing as head of the Better Together campaign, with 32% dissatisfied – giving him a net approval rating of +1.
Ms Sturgeon's approval rating was also higher than the +7 scored by First Minister Alex Salmond, with 50% of voters happy with his performance in the role, but 43% unhappy.
While the proportion of Scots who are satisfied with Mr Salmond has remained at 50% or more for the last 18 months, his net satisfaction rating has fallen from +35 in December 2011.
Labour were celebrating a minor coup as leader Johann Lamont's approval rating, although based on a lower recognition factor, achieved +8.
Just 27% of Scots are satisfied with David Cameron's performance as Prime Minister, while 67% are dissatisfied, giving him an approval rating of -40.
The SNP came top in Holyrood voting intentions, with 43% of those polled saying they would vote for the Nationalists if there was a Scottish Parliament election tomorrow, compared to 35% for Labour, with the Tories and Liberal Democrats having the backing of 13% and 7% of those questioned respectively.
l Labour and the SNP are at loggerheads over the use of the word "separation" after it was banned from the title of a Westminster debate. Scottish Labour insisted it would not stop using the word, despite the ruling. But the SNP – who claim the term is pejorative – insisted a precedent had been set.
The Commons Scottish Affairs Committee uses "separation" in the title of its inquiries into the consequences of independence.
But the word has been barred from a debate due to be held in Westminster Hall. A Commons spokesman said the primary reason was that independence was hypothetical and ministers could not be expected to answer questions on potential scenarios.
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