The YouGov research for the Sunday Times found 51% supported independence, compared to 49% who wanted to remain in the UK.
The results are the latest evidence of a dramatic surge for the Yes Scotland campaign, which has seen the gap between the sides - once regularly in double digits - vanish in a matter of months.
The YouGov poll showed the Yes vote increasing by four points, while No dropped by the same number.
The headline figures exclude those who would not vote or are undecided. With those groups included independence was backed by 47% and staying in the UK 45%.
The two point gap is within the margin of error for such polls, meaning the contest, which climaxes on September 18, is effectively too close to call.
Scotland’s Deputy First Minister Nicola Sturgeon described the poll as “exceptionally positive” but added that the Yes campaign “still has a lot of work to do to win”.
Alistair Darling, leader of the pro-Union Better Together campaign, said the poll “must now serve as a wake-up call to anyone who thought the referendum result was a foregone conclusion”.
The former Chancellor said: “The polls may conflict, but the message I take from them is clear: If you want Scotland to remain part of the UK family you have to vote for it on 18 September. Separation is forever.
“These polls can and must now serve as a wake-up call to anyone who thought the referendum result was a foregone conclusion. It never was. It will go down to the wire. Now is the time to speak up and speak out.”
Rumours about the latest YouGov findings had been swirling for days. The firm has charted a remarkable turnaround for Yes, which has seen them recover from a 22 point deficit in just one month.
Writing in the Sunday Mirror, former prime minister Gordon Brown acknowledged that the referendum battle was proving tougher than some had expected - and laid the blame squarely with the Tories.
“Why has it been difficult to win Scottish votes in support of this principle of sharing that most Scots hold dear?” the Labour MP for Kirkcaldy and Cowdenbeath wrote.
“Many are angry that the Bedroom Tax was imposed upon Scots against their will while at the same time the very wealthy received tax cuts.
“The SNP also claim that the ramifications of any Tory privatisation of the NHS in England will cut budgets in Scotland.
“But English and Welsh people have already given an answer to the SNP claims.
“The answer is that 90% of English people want to keep the NHS public and retain it free at the point of need.
“And the vast majority across the whole UK dislike the Bedroom Tax and would even consider more taxes to make our NHS better.”
He added: “Our union is not out of date or an anachronism or a museum piece but a unique, unparalleled, multinational living partnership that Europe and America cannot match or mirror.
“And what our ancestors built up, no nationalist should be allowed to split asunder.”
A second poll, carried out by Panelbase for Yes Scotland, found that No is leading 52% to 48% when undecided voters are excluded.
The Panelbase poll also found that 47% of women support independence, which Yes Scotland say is a 13 point increase in six months.
Ms Sturgeon said: “These are exceptionally positive and encouraging figures - and the Panelbase poll shows record support for independence among women.
“Yes still has a lot of work to do to win on the 18th, we remain the underdogs, but we approach the final 10 days with huge enthusiasm and confidence.
“A positive finding that everyone can unite on - whether Yes or No - is that overwhelmingly people in Scotland believe that deciding our future in a democratic referendum is something we can be very proud of as a nation.
“The referendum has engaged many people who have never voted before in their lives, filled public halls the length and breadth of the country, and ushered in a sense of possibility and creativity.
“The challenge for all of us is to unite as a country once the decision is made, and do everything we can to maintain this boost in democratic participation that the referendum has ushered in.”