The survey, for Channel 4 News, found that 51 per cent of people questioned are planning to vote No in the referendum.
That compares to 37 per cent of people who said they would be backing independence while 12 per cent said they did not know how they would vote, according to the research by YouGov.
When those who do not know how they will be voting were factored out, the poll found 58 per cent of people are in favour of staying in the UK while 42 per cent said they would be voting Yes.
The research comes after a different poll last month put support for independence at 39 per cent, just three points less than the 42 per cent backing for the Union.
When those who are undecided about how to vote were excluded from that ICM survey, the results put Yes on 48 per cent and No on 52 per cent.
YouGov questioned 1,208 people in Scotland on the issue for its latest research, with the survey carried out between April 25 and 28.
Of those who are planning on voting in favour of independence, 60 per cent said this was because they dislike what Britain has become while 35 per cent said they like Britain, but still wanted Scotland to be a separate country.
A total of 82 per cent of people questioned said they were “absolutely certain to vote” when the referendum is held on September 18.
A spokesman for the pro-UK Better Together campaign said: “This poll is yet another sign that our campaign speaks for the majority of Scots who want Scotland to remain a proud member of the UK.
“People can see the consequences of leaving the UK. We would be giving up the pound as our currency, we would be giving up our membership of the European Union and we would be putting our pensions at risk.
“We believe that we can have the best of both worlds. We can have a strong Scottish Parliament with more powers guaranteed and we can have the strength, security and stability that comes from being part of the larger UK.”
He added: “As encouraging as this poll is, there can be no complacency. The Nationalists only need to win once and by a single vote to take Scotland out of the UK forever. We need everybody who believes that we are stronger and better together as part of the UK to do their bit and get involved.”
Blair Jenkins, chief executive of the pro-independence Yes Scotland campaign said: “The most significant finding in this poll is that more than eight in 10 people say they are certain to vote in the referendum.
“With more than four months to go to the vote, this is a very encouraging indication of the high level of engagement among voters and comes on the same day that research by ScotCen shows that Yes supporters are more likely to vote than those on the No side.
“The headline figures in this poll are almost identical to the last YouGov poll in March. But an ICM poll conducted only last month puts the gap between Yes and No at only four percentage points while a poll of polls for April reveals that Yes needs a swing of just over five points to take the lead.
“There is little doubt that momentum is very much with Yes because more and more people are realising that Westminster simply isn’t working and that putting Scotland’s future in Scotland’s hands makes absolute sense.”