The latest ICM poll put support for Yes on 38 per cent (up four compared with last month) and No on 47 per cent (up two) as the number of undecideds dropped to 14 per cent.
Stripping out the don't-knows, the No campaign's lead over Yes was 55 per cent to 45 per cent, a narrowing of four points over the past month.
ICM quizzed 1,004 people between August 11 and 14, as Alex Salmond faced mounting pressure over his refusal to outline a preferred alternative to his proposal for an independent Scotland to share the pound with the rest of the UK.
A second poll, commissioned by the Yes Scotland campaign and conducted by Panelbase over a similar period, put support for Yes on 42 per cent and No on 46 per cent, with 12 per cent undecided.
Excluding the don't-knows, the No campaign's lead over Yes was 52 per cent to 48 per cent, exactly half the gap recorded by Panelbase at the end of July.
On the two issues which have dominated the campaign over the past week - the currency and Mr Salmond's controversial claim that Scotland's devolved NHS is under threat as a result of health service privatisation in England - the polls brought further encouragement for the Yes campaign.
While 52 per cent of Scots felt Mr Salmond's currency plans were "unconvincing," according to ICM, 45 per cent also believed an independent Scotland would still be able to use the pound in much the same way as now, despite repeated warnings by pro-UK parties that a formal deal to share the currency would not be agreed.
Meanwhile, Panelbase's survey appeared to vindicate Mr Salmond's decision to focus on the NHS.
Asked about "the prospect" that privatisation of NHS services down south would have a knock-on effect on Scottish health budgets, 57 per cent of people said that would make them likely to vote Yes, compared with 43 per cent unlikely.
The warning about Scotland's NHS has been angrily rejected by the pro-UK parties as baseless scaremongering, but has emerged as a key campaign message for the Yes side.
The Panelbase poll also found that leading figures in the Yes campaign were more trusted to "stand up for Scotland" than their opposite numbers in the No campaign.
Nicola Sturgeon, the Deputy First Minister, topped the list, with 53 per cent of people saying they trusted her to fight for the country, ahead of First Minister Alex Salmond, who was backed by 52 per cent of voters.
On the No side, Better Together head Alistair Darling was trusted by 32 per cent of people to stand up for Scotland, ahead of Scots Labour leader Johann Lamont on 30 per cent.
Fewer than one in five people (19 per cent) backed Prime Minister David Cameron.
Writing on the What Scotland Thinks website yesterday, polling expert Professor John Curtice, of Strathclyde University, said the polls did not show clear evidence of new momentum for a Yes vote.
But he added: "The fact that both Panelbase's and ICM's poll strongly suggest that the Yes vote has not declined in the wake of the leaders' debate means that a pro-independence campaign that had appeared to be at risk of being written off by the media will now enter the last month of campaigning with renewed heart - and that interest in and speculation about the outcome of the referendum will remain at fever pitch."
Yesterday's findings left the What Scotland Thinks poll of polls, based on all the most recent surveys, unchanged with Yes on 43 per cent and No on 57 per cent.
Blair Jenkins, chief executive of Yes Scotland, said: "With a month to go until the vote, these are very encouraging polls demonstrating real momentum.
"Yes is up two points in both polls - we are continuing to gain ground and success on September 18 is within Scotland's reach.
"The ICM poll shows that those who were undecided last month - and have now made up their minds - have come to Yes by a margin of two to one."
Better Together campaign director Blair McDougall said: "These two opinion polls show that the majority of Scots are continuing to reject separation as Alex Salmond still cannot outline his currency Plan B.
"In one week, up to one million Scots will start casting their referendum vote by post but Alex Salmond and the Nationalists can't answer the basic questions, such as what currency would be in our pocket or how our public services would be funded."