The Panelbase survey found a record 43% of voters now say they will back independence on September 18, compared to 47% voting No.
The figures are 48% for Yes and 52% for No once undecided voters are removed, suggesting the Yes camp needs just a two-point swing for victory.
The gap between the two sides has halved from eight points to four since last month, when Panelbase put Yes on 46% and No on 54%.
Yes Scotland, who commissioned the new poll, hailed it as a turning point in the campaign. Chief executive Blair Jenkins said: "This is a breakthrough poll, showing support for Yes at a campaign high. It shows our message that only with independence can the wealth of Scotland work for all people is getting through. The No campaign are panicking at the steady closing of the polls and flinging mud, but it isn't working because people want to support a positive vision for Scotland's future.
"And in our view the internationalisation of the debate, with people like President Obama talking about Scotland, and the acceptance across the political spectrum that Scotland needs more powers, are galvanising the Yes vote."
Speaking in Stirling yesterday, deputy first minister Nicola Sturgeon said: "I'm confident that this campaign is neck and neck [with the No side] and that means it's there for us to win."
Sturgeon will tomorrow confirm the draft constitution for an independent Scotland would commit the country to the early removal of Trident nuclear weapons, a promise likely to appeal to the wavering Labour voters seen as critical to the outcome of the referendum.
The Panelbase exercise comes just days after a poll by Survation also found a record level of support for Yes, at 47%, compared to 53% for No.
Pollster Professor John Curtice said the two new polls together suggested that, after a few months in the doldrums, the Yes campaign appeared to be regaining momentum.
However, he also said the gender gap identified in the new Panelbase survey was "enormous", with support for Yes among decided female voters 15 points behind that for men, at 41% against 56%.
A Panelbase poll for Yes Scotland in April put the gap between the sexes at 10 points, with 42% of women backing Yes against 52% of men. He said: "It's women that really are a problem for the Yes side. You get a majority among men, and it's women who drag it [the total] down."
On a more positive note for Yes, support for independence has risen among decided Labour supporters (from 29% to 34%) and middle class ABC1 voters (from 38% to 41%) since Yes Scotland's last Panelbase poll in April.
Prof Curtice said the No camp ought to be worried that its much-vaunted "game-changer" moments, such as a veto on sharing the pound and President Obama's support for the union, didn't appear to be having much effect on voters.
"There's reason for Yes Scotland to be pleased, and reason for Better Together to be worried.
"As ever through this referendum campaign, there's a degree of uncertainty, but you can't discount it as 'wavy lines' [as Better Together once called unhelpful polls], when two companies come up with record poll shares for Yes. The advice to Better Together is, find ways to appeal to people using a far greater sensitivity to the Scottish psyche."
SNP sources last night insisted that the gender gap was closing, with the party hoping for a late burst of support for Yes among women just before polling day, as happened with female support for the SNP in the 2011 election. The First Minister recently suggested the lower level of support for independence among women was due to them taking longer to mull over the issues before making their decision.
The new Panelbase poll also found 55% of voters (discounting don't knows) were more likely to vote Yes if they felt the 2015 general election would produce another Tory-led government at Westminster, and 50% said they were more likely to vote Yes if a Labour government was imminent.
However, Prof Curtice said he was "sceptical" of such questions, as all scenarios helped Yes.
Discounting a poll by Panelbase last August which is now regarded as rogue, the new gap between the Yes and No is the narrowest yet.
The survey of 1060 people aged 16-plus was conducted between June 9 and 11, when both the Yes and No sides ramped up their campaigning for the 100-day countdown marker, and after the three unionist parties said they would give Holyrood more powers in the event of a No vote.
On the last day of the poll, Harry Potter author JK Rowling announced she had given £1m to the Better Together campaign to save the union.
Last week's other high profile interventions - from former US First Lady Hillary Clinton and Pope Francis - came after the poll ended.
Despite being told the gap between Yes and No had narrowed to less than five points, Better Together said: "It's impossible to comment on a poll that's not been shared with us."
Scottish Tory leader Ruth Davidson yesterday told the BBC she might campaign for a currency union with the rest of the UK in the event of a Yes if it was "best for Scotland", just as Chancellor George Osborne would oppose a union in the rest of the UK's interests.
It also emerged yesterday that the English Democrats, a party which campaigns for a devolved English parliament akin to Holyrood, has registered with the Electoral Commission as an official Yes campaigner in the referendum.