The latest TNS-BMRB poll, published today by The Herald, shows those who would vote Yes for independence ahead by 39% to 38%
The last time those who back Scotland going it alone were in front was a one-off lead for independence supporters in spring 2008.
They had trailed those who would vote No in a referendum by 15 points in August 2007, and the 15-point gap had opened up again by November 2009.
By the Holyrood election in May, when the SNP won an outright majority, the gap was down to eight points.
The number against independence is the lowest in any of the polls to date. The number unsure how they would vote, at 23%, is at the second-highest level, which will let both sides claim there is all to play for.
James Mitchell, professor of politics at Strathclyde University, said: “It will encourage the Prime Minister to engage with this issue more seriously. Devolving responsibility to Michael Moore, the Scottish Secretary, may have been the wrong devolution for the Prime Minister to have backed.
“It demonstrates that even before we see the full force of public spending cuts -- which Scots are likely to blame on Mr Cameron’s Government -- there is growing evidence of dissatisfaction with the status quo.”
Chris Eynon of TNS-BMRB said: “For now, the ball is rolling in favour of the SNP and independence. However, a lot can change over the next two to three years.”
The SNP Government has again taken the Cabinet around the country for roadshows and has published demands for extra powers through strengthening the Scotland Bill. The Coalition was painfully slow off the mark in recognising the dangers to the Union posed by an outright majority for Alex Salmond.
In recent weeks a group comprising Mr Cameron, his deputy Nick Clegg, Chancellor George Osborne, Chief Secretary to the Treasury Danny Alexander and Mr Moore was formed to combat this.
The attack on independence at the annual CBI Scotland dinner in Glasgow on Thursday was the first skirmish in the new war.
But on Wednesday the First Minister will present his programme for the next Holyrood session against a backdrop of seriously wounded Opposition parties, the two biggest of which have lame-duck leaders.
In each of the 10 polls, TNS-BMRB has asked the same straight agree or disagree question on the premise “that the Scottish Government should negotiate a settlement with the Government of the United Kingdom so that Scotland becomes an independent state”.
The latest sample of 1007 adults in 69 constituencies took place on doorsteps between August 24-31.
Mr Eynon said: “It does provide a stark measure of how attitudes towards independence per se have moved since the SNP first came to power in 2007.” He added: “The decline in opposition is reflected more in a shift to ‘undecided’ than to ‘support’, which is perhaps not surprising. It would be a major change to move from opposing to supporting independence over a short period.
“What this does suggest is that resistance is being challenged and more people are being encouraged to reconsider their opposition to independence.”
Ipsos Mori, polling last week, had Labour adrift of the SNP at Holyrood by 21 points (49% to 28%) while even for Westminster the SNP led Labour by 42% to 33%.
On Mr Salmond’s personal performance 62% were satisfied, while 28% were dissatisfied.
An aide to Mr Salmond said: “Clearly, the attacks on independence in recent days from the Tory and LibDem UK Government -- far from making a positive case for the Union -- have backfired badly.”