The Yes vote stands at 48 per cent compared with 52 per cent for No, when the undecided voters are excluded, the survey of more than 1,000 voters by ICM found.
When the 14 per cent of voters who have yet to make up their minds were included No support was 45 per cent compared with 41 per cent for Yes.
Published the day before Scotland’s date with destiny, the poll suggested that Yes was gaining ground when the findings were examined alongside a directly comparable survey conducted last month.
An ICM poll compiled in August put support for Yes at 45 per cent when undecideds were taken out – indicating that the Yes campaign has gained three percentage points to 48 per cent.
This has been accompanied by a slip of three percentage points for a No vote which has fallen from 55 per cent to 52 per cent over the same period.
The survey is published as both sides embark on the final day of campaigning before polling stations open tomorrow.
Yes supporters will be hoping that one last big push can take their campaign over the finishing line first.
Better Together, meanwhile, will be attempting to shore up their vote and working to ensure that the undecideds break towards No at the last minute to ensure that its diminishing lead is not eroded. “It is very tight,” John Curtice, Professor of Politics at Strathclyde University said last night.
“At the moment it looks as if the Yes campaign is going to fall agonisingly short from their perspective. But I have always said this is the No campaign’s to lose and it certainly looks as if they have got pretty close to that.”
Last night Better Together’s campaign director Blair McDougall said: “This vote will go right down to the wire. There is no room for a protest vote. If we vote to leave the UK there would be no going back, no matter what it costs us in terms of bigger cuts, higher prices and fewer jobs.
“The last week has exposed how much of a risk going it alone would be for Scotland. Jobs would move to England, funding for pensions would be cut and our NHS would be at risk.
“These are risks we just don’t need to take. We can have faster, better, stronger change for Scotland within the UK. We can have more powers for Scotland without taking on all the risks of separation. If people want to avoid these risks then they have to vote No. It can’t be left to someone else.”
Meanwhile Blair Jenkins, chief executive of Yes Scotland, said: “This is hugely encouraging for Yes - the six-point narrowing of the gap since the last comparable poll shows that Yes has the momentum as we approach referendum day.
“People know that a Yes vote is Scotland’s one opportunity to achieve job-creating powers, protect our NHS from the damaging impact of Westminster cuts and privatisation, and ensure that never again do we get Tory governments imposed on Scotland that we have roundly rejected.
“This poll - like all the recent polls - shows we are in touching distance of success. The referendum is on a knife edge, and this will spur on everybody who wants and is working hard for a Yes to redouble their efforts.”
There was some comfort for the Better Together campaign when “undecideds” were asked which way they were “more likely” to vote when they finally make it to the booths tomorrow.
Twenty per cent said they were more likely to favour No and 12 per cent were more likely to favour Yes. The remainder were still uncertain as to which way they would eventually go, suggesting there will be a desperate battle to win them over as the hours tick down to the big day.
The poll, which was carried out between September 12 and 16, also showed that capturing the female vote could play a decisive role in determining the outcome, even at this late stage.
According to the survey, 16 per cent of women were still undecided compared with 12 per cent of men.
When undecideds were included, women were still more sceptical about independence than men.
Thirty-seven per cent of women were Yes voters compared with 45 per cent of men.
Forty-seven per cent of women said they would vote No, compared with 43 per cent of men.
The poll also suggested that the pro-Union parties promise of more powers for Holyrood had made an impact on the campaign.
Almost half (49 per cent) of those surveyed felt the Scottish parliament would be given more powers in the event of a No vote. That was higher than the 26 per cent, who felt that Holyrood’s powers would remain the same if independence was rejected and the 13 per cent who felt Holyrood would lose powers.
Once again, the economy emerged as a key issue with 45 per cent of those surveyed believing that independence would be bad for the economy compared with 38 per cent who thought it would be good. Ten per cent did not know what effect breaking up the UK would have on the economy and six per cent thought independence would make no difference.
When it came to alleviating poverty, 37 per cent thought that there would be less inequality in an independent Scotland – a higher number than the 20 per cent who thought there would be more unfairness.
The poll is published as both sides kept up the momentum on the campaign trail yesterday.
The Labour leader Ed Miliband was forced to abandon a walkabout in an Edinburgh shoppping centre after his band of supporters clashed with a noisy group of Yes supporters. Earlier Mr Miliband had joined with the other leaders of the UK parties David Cameron and Nick Clegg to sign a vow for “extensive” new powers to be transferred to Holyrood in the event of a No vote.
Alex Salmond, meanwhile, has appealed to Scots to seize the chance to wake up on Friday to the “first day of a better country” in an open letter addressed to the nation.The First Minister argued that Scotland has “changed forever” and urged voters not to let the chance for independence to slip through their fingers.