The survey by the Scotland in Union organisation found 59% would vote to remain, while 41% would back independence. But the findings were dismissed by the SNP Deputy leader Keith Brown who claimed the question was "rigged."
Instead of "Should Scotland be an Independent Country?", it asks "Should Scotland remain in the United Kingdom or leave the United Kingdom?"
Most polls recently have indicated that opinion among Scots was split down the middle in the independence issue.
The Survation survey also found 27% of people support Nicola Sturgeon’s plan for a second referendum within 18 months, while 87% of those who don’t want another referendum believe the 2014 contest was a ‘once-in-a-generation’ event.
Pamela Nash, chief executive of Scotland in Union, said: “Just five years on from the referendum that Nicola Sturgeon promised was a ‘once-in-a-generation’ contest, this landmark poll shows that 59 per cent of people in Scotland want to remain in the UK.
“More than half a million Scots who voted ‘Yes’ in 2014 have now switched to supporting Scotland’s future in the UK to protect vital public services like the NHS and schools from the SNP’s drastic cuts.
"People are seeing the chaos that Brexit has brought, and know that Scotland leaving the UK would be much worse."
Among former ‘Yes’ voters who now want to remain in UK, ‘protecting public services’ is the most popular reason for changing their vote, while 49% cite Nicola Sturgeon’s performance as First Minister.
60% of voters in Glasgow now support remaining in the UK.
But the survey was branded "desperate stuff" by Mr Brown who accused the pro-union campaign of "running scared."
"They are now trying to rig the question too, in a deliberate bid to confuse independence with Brexit in the minds of voters," he said.
"Yet even this panicked attempt to skew things their way has backfired spectacularly - with this poll showing almost two-thirds of people are now in favour of another independence referendum.
"Polling consistently shows support for independence up since 2014 – with most recent polls showing a referendum result is too close to call. More and more people are seeing the Westminster chaos which is failing Scotland, and are turning to independence. Momentum is building towards a referendum, and when it comes, all the signs are that the people of Scotland will vote Yes.”