Overall, the latest Ipsos MORI survey for The Times found that among those who are certain to vote in next year's independence referendum, 34% backed Scotland leaving the UK - up from 30% in October.
Support for Scotland staying in the union fell slightly, going from 58% to 55% over the same period.
But the poll showed a large rise in support for independence amongst voters aged 18 to 24.
This stood at 27% last October but in the new survey - which was carried out between February 4 and 9 - this had increased to 58%.
The latest figures showed 43% of people in deprived areas backed independence while 65% of those living in more affluent parts wanted Scotland to stay part of the UK.
Support for the union was also stronger among females, with 61% of women favouring this while 41% of men supported independence.
A total of 1,003 people in Scotland were questioned for the research, which also gave Deputy First Minister Nicola Sturgeon a higher approval rating than the man leading the campaign to keep Scotland in the UK.
Ms Sturgeon, who is spearheading the campaign for independence, came out with a net approval rating of +17, with 50% of those surveyed satisfied with her performance compared to 33% who were dissatisfied.
Meanwhile 33% of people said they were satisfied with the job former chancellor Alistair Darling is doing as chair of the Better Together campaign, with 32% dissatisfied, giving him a net approval rating of +1.
Ms Sturgeon's approval rating was also higher than the +7 scored by First Minister Alex Salmond, with 50% of voters happy with his performance in the role, but 43% unhappy.
While the proportion of Scots who are satisfied with Mr Salmond has remained at 50% or more for the last 18 months, his net satisfaction rating has fallen from +35 in December 2011.
Just 27% of Scots are satisfied with David Cameron's performance as Prime Minister, while 67% are dissatisfied, giving him an approve rating of -40.
Mr Salmond's SNP came top in Holyrood voting intentions, with 43% of those polled saying they would vote for the Nationalists if there was a Scottish Parliament election tomorrow.
A total of 35% said they supported Labour, with the Tories and Liberal Democrats having the backing of 13% and 7% of those questioned respectively.
Mark Diffley, director at Ipsos MORI Scotland, said: "Our latest poll shows a boost in support for those campaigning for Scottish independence, who will take some encouragement from these findings.
"Having said that, support for independence is behind where it was a year ago and those campaigning for Scotland to remain in the UK retain a sizeable lead.
"The campaigns are entering new phases, with a greater emphasis on the issues of substance that will be key in deciding the outcome of next year's vote.
"With this in mind, this poll provides detail on where the two campaigns are strongest and weakest, allowing them to see where they need to concentrate their efforts."
Blair Jenkins, chief executive of the pro-independence Yes Scotland campaign, said: "The support for an independent Scotland among 18-24-year-olds has more than doubled in the last four months, showing very clearly that our positive and optimistic campaign is resonating with younger people who have the greatest stake in securing a fairer and more prosperous future for our country.
"This poll is also very good news for Yes because support for a Yes vote in 2014 is on the way up while those intending to vote No is on the way down, and this is consistent with other recent surveys."
He added: "It is becoming increasingly clear that Westminster isn't working and as we continue to make the positive case for an independent Scotland we are confident the polls will continue to move in our favour."
Mr Darling said: "Being ahead in the polls is always better than being behind.
"However, there is no doubt that the only poll that matters - and the poll that we are absolutely focused on is the one that will be taking place in autumn next year.
"We will be doing everything we can between now and then to win the arguments, and win the votes of people in every part of Scotland."
SNP business convener Derek Mackay said it was an "excellent poll" for the Nationalists.
The local government minister stated: "For SNP support to be increasing almost six years into office, and be around the same level which delivered our landslide victory in 2011, is a fantastic achievement by any standard.
"The increase in support for an independent Scotland - narrowing the gap with No by seven points since last October - is extremely encouraging."
Mr Mackay said: "The political landscape is changing in a way which is boosting the case for a Yes vote - not least as the damaging impact of Westminster's ill-thought out and unfair benefits cuts become sadly clear.
"The compelling case for a Yes vote is that only with independence will Scotland always get the governments we vote for, and we are confident but by no means complacent about achieving success in the referendum."