The YouGov poll recorded the highest level of backing for a Yes vote in its polling on the referendum question, although No support maintained a 14-point lead.
It puts support for independence at 43%, with 57% backing the Union, excluding undecided voters.
YouGov polling from earlier this month put the figures at 39% for Yes and 61% for No.
The poll of more than 1,000 people between August 12 and 15 also found an increase in the proportion of voters who believe an independent Scotland would be better off, up from 27% in June to 32%.
The proportion of people who believe the country would be worse off fell from 49% to 46% over the same period.
The latest poll shows 44% of Scots think that Westminster parties are bluffing by ruling out the Scottish Government's favoured option of a currency union between an independent Scotland and the rest of the UK, compared with 40% who believe the assertions.
YouGov found 45% back a currency union, 23% want a separate Scottish currency, 6% support the euro and 8% back a sterlingisation model.
The findings follow weekend polls that showed a similar move in support for independence.
An ICM poll of more than 1,000 people for the Scotland on Sunday newspaper put Yes backing at 45% and No at 55%, when Don't Knows were excluded.
Meanwhile, another poll by Panelbase, commissioned by the Yes campaign, reported findings of 48% for Yes and 52% for No when undecided voters were removed.
First Minister Alex Salmond said the recent spate of polls show the Yes campaign has a "spring in their step".
He told BBC Radio Scotland's Good Morning Scotland programme: "We've now had three opinion polls over this weekend showing significant gains for the Yes campaign.
"One of the things that the polls today indicate is it is moving in our direction. Firstly, the vast majority of people in Scotland want to keep the pound and a majority of people don't believe the Westminster attempt to say they'll seize all the UK financial assets.
"I think it's actually becoming more clearly understood that we can't actually be stopped from using the pound. What they're talking about is seizing the assets of the Bank of England and not giving Scotland any share, in which case of course they would have to stump up on the national debt."
Better Together campaign director Blair McDougall said: "This is yet another poll confirming we speak for the majority of Scots when we say 'No thanks' to the risks of independence.
"With just over one week until the postal votes of up to one million people are delivered, Scots still don't know what currency we would use in a separate Scotland. We don't know what money our wages, pensions or benefits would be paid in and we have no idea what currency we would use to pay for our schools and hospitals. It all means independence isn't a risk worth taking.
"There can be absolutely no complacency from those of us who believe the brightest future for Scotland is to remain in the UK."