The shift has been picked up by the same polling system that identified the surge which swept the SNP to an unprecedented majority in the 2011 Holyrood elections.
While those campaigning for a No vote are still in the lead, Yes Scotland believes there is evidence of growing support for independence among what is seen as two key groups of the electorate.
"This new, robust research is based on a sample several times the size of a conventional poll," said a Yes Scotland strategist.
"This bespoke polling is based on a well-designed series of questions building on a rolling monthly basis going back to last January."
The pro-independence campaign believes voter engagement is the key to success. The more interested people are, they say, the more open they are to persuasion of the merits of a Yes vote.
The polling found 74% say they are interested in the debate, compared to 10% who say they are not interested. Another indicator of engagement is intention to turn out on referendum day, with 75% saying they are "very likely to vote" and a further 13% saying they are "quite likely to vote."
The source said: "We believe engaging people's interest is key to building support. The more information people want they better it is for our side of the campaign."
The new research is significantly different from other recent polls in showing that women are no more likely to be No voters than men. It indicates men and women are equally likely to oppose independence.
Women are, however, more likely to be undecided, but as their minds are being made up more are supporting Yes than No, the Yes camp says. The polling uses a one-to-ten scoring system with one or two being most opposed to independence and nine or ten being keenest on it.
Women are said to be shifting steadily up the scale, according to this research.
The other surprise finding also contradicts recent polling in finding the strongest support for independence among those aged 16-24.
"There is now a majority among these young voters in favour of Yes," it was claimed.
The other area of strength for the pro-independence cause is among parents with children aged 11 to 15, where there is also a majority in favour.
Polls have suggested SNP leader Alex Salmond has failed to connect with women in the same way as he has with men.
Winning over the female vote for independence is a key task of the Yes campaign. The appointment of Nicola Sturgeon to lead the campaign was seen by independence supporters as a way of winning favour with women.
But recent polls suggested the task remains considerable. Last month, an Ipsos MORI poll had support among women for independence at only 23%, down by five points on February, despite a concerted effort by the SNP to woo women voters with promises of better childcare if they vote yes.
Yes Scotland will continue aggregating the polling material in the months to come.
It will be shared with the various sub-groups within the campaign and with groups such as the Scottish Independence Convention to inform the way they seek to build support.
As unverified, external polling it will be dismissed by pro-Union campaigners.
However, Yes Scotland said it had used the same system that had accurately identified the SNP's 2011 victory.