The poll, by Savanta ComRes for The Scotsman, interviewed 1,001 Scottish adults between April 23 and 27.
The survey showed support for Yes at a low of 42 per cent if a second independence referendum was held tomorrow, with No on 49 per cent.
With don’t knows excluded, this would see the unionist side win indyref2 with 54 per cent of the vote against 46 per cent from the pro-independence side.
The survey also showed the SNP losing seats and down to 61 overall, although Holyrood would still see an overall pro-independence majority with 11 seats predicted for the Scottish Greens.
Responding to the poll, Alistair Carmichael MP called on pro-union voters to back the Liberal Democrats.
He said: "The public can clearly see that putting an independence referendum before the recovery is a fool's errand.
"If you've voted nationalist in the past, but want to see the next government focused on education and mental health, you should back the Liberal Democrats. If you are a green voter who wants the focus to be on the climate emergency not independence, you should back the Liberal Democrats.
"If you're voting Alba, you're probably a lost cause."
Pamela Nash, the chief executive of pro-union campaign group Scotland in Union, said it was clear the majority of Scots did not back independence.
She said: “It is an important reminder that whatever claims the SNP makes after next week’s election, a majority of Scots do not want to leave the UK.
“The strength of the UK has been invaluable for Scotland and all the nations and regions during the past year.
“We faced this challenge together, leaving no community behind while we tackled Covid.
“We must now take that same approach to the recovery, working together for every community across the UK in the years ahead rather than dividing Scotland once again.”
Keith Brown, the depute leader of the SNP, said the poll showed the election was on a “knife-edge”.
He said: “This poll confirms the election result is on a knife-edge in terms of whether the SNP secures a majority.
“The only guaranteed way to ensure Nicola Sturgeon is re-elected as First Minister, to put recovery in our own hands and to prevent Boris Johnson from deciding Scotland’s future, is to give both votes to the SNP on May 6.”
At a virtual press conference, Anas Sarwar said it was clear the momentum was with his party.
Scottish Labour was up three points to 23 per cent in the constituency vote and up two points to 19 per cent in the list.
The leader said: "I think you can see that we are the ones that are rising in the polls, both in the constituency vote and the regional vote, and our message is cutting through to the public about not going back to those old arguments.
"I have been very clear on my position. I don't support independence, I don’t support a referendum, but I want us not to be a party that only speaks to the half of the country that agrees with them on the constitution.”