The survey puts backing for a split from the UK at just 25%, down five points since a similar poll in March.
However, it was matched by a four-point drop in support for a No vote, to 47%, and a big surge in the number of don't-knows, prompting pollster TNS to declare the race wide open.
The findings were released hours after the First Minister outlined details of his Government's law-making proposals in the run-up to next year's historic vote. He told MSPs his plans for the coming year showed Scotland should be governed from Holyrood and not Westminster.
The TNS BMRB survey of 1017 adults, conducted between August 21 and 27, came as MSPs returned to Holyrood after their summer break.
The poll showed both camps in the referendum battle losing support.
The number of undecided voters rose to 28% from 19% in March and 15% in February. Yes Scotland, the pro-independence campaign, said it would be "doubling its efforts" to target the don't-knows, while rival Better Together accepted it needed to "work hard" to get its message across.
Tom Costley, of TNS Scotland, said: "The surge in the number of those who have not decided how to vote may have arisen because both campaigns have succeeded in giving rise to doubts among some who have previously backed the other side, without generating positive support for their positions.
"With so many undecided, there is still all to play for. The high number of don't-knows could turn out to be the most significant factor in how the referendum campaign develops."
He added: "Both the Yes and No camps have lost ground in 2013, which suggests neither campaign has yet succeeded in making a strong connection with the voters in Scotland."
The 25% who say they will vote Yes marks the lowest level of support for independence since TNS BMRB began polling on the issue in 2007. Before the wording of the referendum question was finalised this year the pollster asked whether respondents agreed that Scotland should negotiate on independence.
Over the period, support for independence reached a high of 39% in August 2011, shortly after the SNP's landslide Holyrood election victory.
The latest poll put support for independence at 30% among those certain to vote. Backing for the UK was 51% among those certain to vote. Overall, 62% of Scots said they would definitely vote on September 18 next year.
The poll follows two recent surveys that showed wildly different results.
A YouGov poll at the weekend put support for a Yes vote at 29%, No on 59% and just 10% undecided.
However, a Panelbase survey commissioned by the SNP gave the Yes camp a narrow lead over the pro-UK side - 44% to 43% among those certain or highly likely to vote.
The outcome of both polls is thought to have been influenced by other questions put to voters before they were asked their view on independence.
Yesterday the SNP published further details from its Panelbase poll showing more Scots were likely to vote for independence if they believed the Conservatives would return to power at Westminster in 2015.
Responding to the latest survey, Yes Scotland chief executive Blair Jenkins said: "The most significant figure in the TNS poll is the increase in the number of people who are undecided.
"We know from our own research that the more people learn about independence the more likely they are to vote Yes because they realise that having a government they vote for in Scotland is the best way to build a fairer, more prosperous country.
"So over the next 12 months we will be doubling our efforts to provide the quality information people need to help them make the right choice."
Better Together campaign director Blair McDougall said: "Alex Salmond's independence campaign has lost one in three supporters since 2011. Almost half of SNP voters are not currently supporting independence.
"But whatever a poll says, our message is always the same: we need to work hard to reach out to undecided voters. We will never take the support of Scots for granted."