The Survation study of 2,000 adults, commissioned by The Courier, also found that a majority of Scots would only vote for independence if membership of the EU was guaranteed.
Conducted between March 11 and March 18 - before James Hamilton’s report cleared the First Minister of breaching the ministerial code - the poll found the SNP would win 50 per cent of the constituency vote and a 39 per cent share of the regional list second vote.
While the Tories would take 21 per cent of of the constituency vote - compared to Labour’s 20 per cent - Anas Sarwar’s party would take slightly more of the regional list vote (20 per cent versus 19 per cent).
A seat projection based on the survey results would see the Tories’ share of seats collapse by almost a third, down from 31 to just 22
At the same time, the SNP would win a small outright majority of 67 - while Labour returned to Holyrood as the main opposition on 24 seats.
The projection would see the Scottish Greens gain the most new seats of any single party – an increase of five – bringing their total to 11.
The Lib Dems would take fifth place overall, retaining their current tally of five seats.
Polling expert, Professor Sir John Curtice said of the results: “There really is a close race for second place.
“Basically 27 per cent of current SNP voters say that they might vote Labour, but only 6 per cent say they’d vote Conservative.
“Equally 23 per cent of Labour voters and 24 per cent of Lib Dem voters say they might vote for the SNP.
“The dirty secret of this election is going to be, for the UK government to avoid the embarrassment of the SNP having an overall majority, they are relying on the Labour Party to deliver it.”
Despite the good news predicted for the SNP, the polling suggested that enthusiasm for Nicola Sturgeon and the party in general is not translating into greater support for Scottish independence.
Survation’s survey found 51 per cent of voters would say No if asked “should Scotland be an independent country?”.
But, if membership of the European Union was guaranteed, support for Yes rose to 53 per cent.
Professor Curtice said the row over the Alex Salmond inquiry seemed to have had little effect on the numbers.
“All the polls are roughly around 50/50 at the moment and there is increasing evidence the whole row has not made much difference.
“Support for the country is split down the middle of the country and has been split down the middle since February.
“It’s clearly lower than it was last year, but it hasn’t really moved during the course of recent weeks.”
He added: “The support for independence amongst people who voted remain goes up from 54 per cent in the standard question to 59 per cent, whereas the leave voters basically aren’t moved.
“So it basically attracts more remain voters, which is already the case, support for independence is quite heavily structured by whether people voted remain or leave in 2016.”