The exclusive poll, conducted by Savanta ComRes for The Scotsman, suggests Nicola Sturgeon’s party could be set for a shock result, leaving them well short of a majority.
Such a result would see the pro-independence party returned to government with 59 MSPs after 14 years in power and short of a majority by six seats.
They would still retain an overall pro-independence majority alongside the Scottish Greens if similar figures are returned after polling day on Thursday.
The survey also continues a general downward trend for the SNP in this series of polls, but indicates a lower level of support for the nationalists compared with other surveys and is the lowest since an October 2019 poll by Panelbase.
Such a result would be “ultimately a dominant performance”, according to polling experts, and the figures should be viewed in the context of sky-high figures for the SNP towards the end of last year.
The poll interviewed 1,001 Scottish adults aged 16 or over between April 30 and May 4.
The results come in contrast to two polls reported on Tuesday that showed the SNP returned a majority.
Research by Opinium, commissioned by Sky News, had the SNP on track to secure a slim majority of 67 seats, while a YouGov poll for The Times suggested the party was set to secure a four-seat majority.
Scots are, however, still broadly split over independence, with this survey the second in a row from Savanta ComRes to measure a clear gap between Yes and No.
Overall, 50 per cent of voters said they would vote No if a second independence referendum was held tomorrow, with 42 per cent saying they would vote Yes with a further 8 per cent undecided.
With don’t knows excluded, the poll puts support for the union at 54 per cent and support for independence at 46 per cent.
Ms Sturgeon’s party received just 42 per cent of the constituency vote in the poll, which could be a cause of concern within SNP headquarters ahead of polling places opening on Thursday.
The party’s list vote of 34 per cent is just three points higher than what it received in 2007.
Such a result would see the SNP return 59 MSPs, down four on their 2016 result of 63, with the list vote failing to make up for potential losses in the constituency.
However, the unionist parties are unlikely to make major gains despite this drop in SNP support.
Scottish Conservatives are backed by 25 per cent of voters on the constituency ballot, with 22 per cent backing Douglas Ross’s party on the regional list, up two and one point respectively from the last poll in this series.
Anas Sarwar’s Scottish Labour is backed by 22 per cent and 19 per cent respectively, up one point on the constituency ballot and with no changes on the regional list.
If this poll is replicated in the results, Mr Ross is likely to lose one MSP from his cohort, leaving him with 30.
Labour would be strengthened with two additional MSPs, increasing their representation from 24 to 26.
It is another strong poll for the Scottish Greens, with much of the ‘other’ support on the constituency ballot going to Patrick Harvie and Lorna Slater’s party.
Their performance of 9 per cent on the regional list – down 1 per cent from the previous poll – would likely return a total of nine MSPs in what would be the party’s record performance at a Holyrood election.
The Scottish Liberal Democrats are set to return all five of their existing MSPs to the Scottish Parliament, but could stage a surprise if local support is strong in places such as Caithness.
Constituency support of 8 per cent (up one point) is among the party’s highest polled support, with 6 per cent (also up 1 per cent) of voters backing Willie Rennie’s party on the regional list.
Alex Salmond’s new venture, the Alba Party, is set to fail to make a breakthrough, the poll suggests, with just 2 per cent of Scots backing the party on the regional list.
This would lead to zero MSPs being elected to Holyrood from the new pro-independence party.
The poll also asked voters whether the return of the former first minister with Alba had made them more or less likely to support independence.
Overall, just 9 per cent of voters said it had made them more likely, with 40 per cent stating it had made them less likely.
For 2014 referendum voters, a quarter (25 per cent) of Yes voters said Mr Salmond’s return made them less likely to vote Yes, with 17 per cent stating it had made them more likely.
Just 2 per cent of No voters said the same, with 60 per cent stating it had made them less likely to back independence.
A total of 27 per cent of those who did not vote in 2014 said the same, with 11 per cent stating Alba made them more likely to vote Yes.
Chris Hopkins, associate director at Savanta ComRes, said the polling figures were bad for the SNP in relation to the sky-high numbers of pre-Christmas.
He said a result along the lines of this poll would be “ultimately a dominant performance” despite likely disappointment around the margin of victory.
The pollster said: “If these polling figures play out on Thursday’s vote, it’ll likely leave the SNP short of the majority they desire and is a fair reflection of a 2021 in which the UK Government performance, and a new Scottish Labour leader, have helped shore up the vote in Scotland for the main unionist parties.
"Falling a little short of a majority is still ultimately a dominant performance from the SNP, and their disappointment should only be felt in the context of significant poll leads towards the end of 2020, where a disastrous year for a new Conservative government in Westminster, a lack of a Brexit deal and the first of murmurings at dissatisfaction with Keir Starmer were contributing to unprecedented numbers for the SNP and for independence.
"However, with some constituency races very tight, these numbers do not even necessarily present bad news for the SNP, and if the drop in support we’ve seen in 2021 can be restricted to areas they’re already strong, Thursday could still yield a strong, pro-independence feel to Holyrood when MSPs return.”