The survey, commissioned by Scotland on Sunday newspaper, shows that 37% of people will vote yes in the referendum, while 44% will vote no.
A further 19% of voters said they do not know how they will vote.
The poll was conducted by ICM between January 21 and 24, surveying over 1,000 people over 16.
It shows a significant rise in support for a yes vote, compared with ICM's last poll on Scottish independence, conducted in September last year before the publication of the Scottish Government's white paper.
In the September poll, 32% of people said they would vote yes, 49% said they would vote no, and 19% said they did not know.
The 5% swing towards a yes vote was described as "a very significant swing" by pro-independence campaigners Yes Scotland.
The poll revealed that support for independence stands at 46%, while 54% want to remain in the union when undecided voters are removed.
This compares with 40% for yes, and 60% for no in the September 2013 poll.
The figures suggest undecided voters remain crucial in determining the outcome of the ballot.
The ICM data also reveals gains for the yes camp among women voters, with support recorded at 33% in the latest poll, compared with 28% in September.
The most dramatic change in voting intentions comes in the 16-24 age group.
The poll shows a 26 percentage point change towards a yes vote, with 44% saying they will vote for independence, compared with just 18% in September, and 33% saying they will vote no, compared with 59% in September. Those who don't know remain static at 23%.
Blair Jenkins, chief executive of Yes Scotland, said: "The poll represents a very significant swing to Yes and shows that we need just over a three percent swing to take the lead.
'It is particularly encouraging that there is a five point increase in support from women, and a four point rise in the number of people who believe independence will be good for the economy is also a welcome shift in our favour.
'The message, too, is getting across that by taking Scotland's future into Scotland's hands we can build a fairer and more equal country. We can also build a more prosperous country where our vast wealth and resources are used more effectively.
"The fact that an increasing number of people believe pensions will be higher in an independent Scotland helps underline that point."
He added: "Significant numbers of people will by now have had a chance to assess the Scottish Government's White Paper for an independent Scotland. That, along with the quality information that we and other groups within the Yes movement continue to produce, sets out a compelling vision of what an independent Scotland can be like.
"People are now also carefully weighing up the consequences and costs of a No vote and, as a result, support for Yes increases."
Deputy First Minister Nicola Sturgeon said: "This is extremely encouraging - with eight months to go this poll shows that our positive message is making significant progress, and a swing of just over 3% will put Yes ahead.
"The rise in support for Yes comes after many people will have taken the time to digest the 'Scotland's Future' document, and strongly suggests that the detailed information on how we can use the full powers of an independent Scotland to transform childcare is encouraging more women and men to vote Yes."
Commenting on the poll on Sky News, Better Together leader Alistair Darling said he believes the referendum will be "far closer than people think".
He said: "I think actually as we get closer to the reality of a referendum (the polls) will be closer," he said.
"What people have to realise of course is that the result in September will be irrevocable," he said.
"Once Scotland votes for independence there is no going back. It's all to play for really."
Speaking on BBC Scotland's Sunday Politics programme, Labour's shadow foreign secretary Douglas Alexander warned that the sample size of the 16-24 age group was small, but he said he was not complacent.
Mr Alexander, who was speaking about the youth vote, added: "What that poll suggests to me is that all of us have more work to do in the remaining 235 days.
"There are no grounds for complacency."
He said: "They (young people) are comfortable with the idea of a layered identity...like many of us are pragmatic in terms of the modern world, where we are interconnected in a way unimaginable a generation ago."