The latest research by YouGov found 37% of people questioned said they support independence, up two points from last month, with 52% planning to vote No, down by one point.
One in 10 people were undecided about how to vote on September 18, while 1% said they would not be voting, according to the poll for The Times.
When this group was stripped away, support for a Yes vote was 42% - the highest support for independence YouGov has reported - with 58% backing the union.
Almost a third (30%) of the 1,072 people questioned said Scotland would be better off economically if it left the UK, while 45% said such a move would be bad for the economy.
Professor John Curtice from Strathclyde University said although the rise in the Yes vote was "modest" it was "still notable".
He said 10 polls had now been published since Chancellor George Osborne and his Labour and Liberal Democrat counterparts ruled out a currency union between an independent Scotland and the rest of the UK, and added: "On average these have put the No side on 43%, up two points on the equivalent statistic for all those polls conducted between the beginning of January and the currency intervention. Between them they represent the best sequence of results for the Yes side yet."
Blair Jenkins, the chief executive of the pro-independence Yes Scotland campaign, said on average the five polls published this month put support for independence at 44%, "halving the gap with No since last November, which is an extremely encouraging direction of travel".
He added: "'We are confident that we will continue this progress and achieve a Yes vote in September, with the compelling message that Scotland can, should and must be independent.
"The steady rise in support for independence - against a drop in backing for No - indicates that the positive message is getting through. All the evidence we have is that the warnings and threats from the Tories and their allies in Labour and the Lib Dems are backfiring on the No campaign."
Mr Jenkins argued: "Only a Yes vote can deliver real opportunity for Scotland. We know we have work still to do over the next six months to convince more people that Yes is the right choice for them, their families and for Scotland - but this poll shows that we are moving steadily in the right direction."
Blair McDougall, the campaign director for the pro-UK Better Together group, said: "It is encouraging that there is a clear majority in favour of Scotland remaining in the UK, despite the nationalists spending millions of pounds advertising their propaganda.
"Given Alex Salmond's failure to tell Scots what would replace the pound, how our pensions would be paid or whether we would be in the EU, it's unsurprising that less than one in five Scots think they'd be better off if we separated from the UK."
Mr McDougall insisted they were "confident but not complacent" in the run-up to the referendum, and would be working to "convince those who have yet to make up their mind that we are stronger and better together".
He added: "We will be setting out the positive reasons why we believe Scotland can have the best of both worlds - a strong Scottish Parliament, with the guarantee of more powers, without losing the strength, stability and security of being part of the larger UK economy. We don't need to put this at risk."