Panelbase found a breakdown of Yes 41% and No 46% when voters were asked the referendum question, with 14% saying they did not how how they would vote on September 18.
The figures suggest a gain of four percentage points for Yes since a similar poll by the same organisation last October, but No also up one point, while Don't Knows were down three points. Totals were rounded up.
Panelbase was commissioned by the independence-supporting website Wings over Scotland.
The site didn't say how many people were polled or when. It said if the Don't Knows were excluded, the margin would be Yes 47-No 53.
Panelbase also carried out a poll for Newsnet Scotland, another independence-supporting site, last month, when the split was Yes 40-No 45-Don't Know 15.
Blair Jenkins, chief executive of Yes Scotland, said: "What this poll clearly indicates is that 'Project Fear' is failing and that increasing numbers of people are realising that Yes promises a better future for themselves, their loved ones and for Scotland.
"With just over five months still to go to the referendum, this poll shows support for Yes has increased to 41%, the highest yet in the campaign - despite all the recent scaremongering and bluffing from the No campaign. The fact is the No camp has played what it believed to be its ace card on currency - which was comprehensively debunked by a Westminster minister last weekend."
Mr Jenkins added: "The results of this poll continue the trend we are finding of an ever-narrowing gap in voting intentions - down to single figures and halved from those of November. All that is required for a Yes vote is a three-point swing."
Deputy First Minister Nicola Sturgeon said: "We take absolutely nothing for granted, but Yes now needs a swing of only three percent to win, and we are confident of achieving a Yes vote in September.
"Alistair Darling and the No campaign have serious questions to answer about their bluff over the pound, but he seems to be burying his head in the sand and incapable of shifting from what is a deeply negative campaign."
Mr Darling meanwhile played down any significance of the Panelbase results, which he described as "something of an outlier in Scottish polls".
He told the BBC's Andrew Marr Show: "If you look at the change from this month to last month, it hasn't changed one bit. Our lead is exactly the same.
"Every single poll conducted this year and last year as well shows us with a consistent lead.
"The majority of people in Scotland are against independence. I believe we will win this, provided we get across our arguments about the benefits of the UK to Scotland and we make our arguments strongly.
"There is a very strong, powerful case for staying part of the UK in terms of jobs, in terms of opportunities, in terms of the ability of us in Scotland as a country to improve people's standard of living, to make sure we have a fair and just society.
"We have strong bonds of culture, of kinship, of family, a shared history of 300 years.
"There is a powerful case for staying in the UK to be made and we will continue to make it."
Mr Darling said Better Together was setting out the positive case for remaining part of the UK and said there had been, on the contrary, "disgraceful" behaviour from some independence supporters.
He said: "Actually, the negativity is largely coming from the Nationalists, who in the last week alone, when anyone speaks out against them, they monster them.
"We had a businessman earlier in the week who said that he thought staying in the UK was good for his business. The behaviour towards him was disgraceful. It brought shame on Scotland.
"We are the ones who are being positive about the case for the United Kingdom."
The former chancellor went on: "In many ways (it's) the best of both worlds where we have a strong, devolved Scottish Parliament with powers over things like health and education, but also we recognise it's in the interests of us all - Scottish firms and businesses in particular - to be able to have ready, unimpeded access right across the UK, no regulatory difficulties, no currency difficulties or anything like that."
Voting analyst John Curtice says on his blog, What Scotland Thinks: "The poll cannot be cited as evidence that there is now a nationalist bandwagon moving continuously and relentlessly towards the 50% mark.
"We should remember that all of the polls Panelbase conducted last year already put the Yes tally at 44% or 45%.The two to three point increase in Yes support since then is simply in line with the trend that has already been evident in more or less all the polls for some two or three months.
"On the other hand, the No side's continuing efforts at persuading Scots of the risk of independence - together with three weekends of unionist Scottish party conferences - are still evidently failing to bear any fruit. The argument that the No campaign is too relentlessly negative will doubtless continue to be heard.
"Better Together will certainly be hoping the persistently relatively high Yes vote in Panelbase's polls is an overestimate of the level of support for independence, though of that there is far from being any guarantee."