The TNS Scotland poll shows the Nationalist up two points on 54 per cent while Labour has dropped two points to 22 per cent.
And based on the poll, the Nationalists could win every Westminster seat in Scotland bar two - Glasgow North East and Orkney and Shetland, currently held by Labour’s Willie Bain and the Liberal Democrats’ Alistair Carmichael respectively.
According to the poll, the Lib Dems and the Conservatives are unchanged on 13 per cent, and six per cent.
Ukip and the Greens are both on two per cent, with the former having gained a point and the latter down one point.
Additionally, in the survey of 1003 adults in Scotland, more than two thirds - 67 per cent - said they were certain to vote, a higher figure than the rest of the UK, where 62 per cent confirmed they would definitely be voting.
However, 29 per cent of voters said they were still undecided.
Respondents were also asked who they felt would get the best deal for Scotland at Westminster, with 42 per cent saying Nicola Sturgeon.
Jim Murphy was second on eight per cent; David Cameron on seven per cent; former First Minister Alex Salmond on six per cent and Labour leader Ed Miliband on three per cent.
And among SNP supporters, 81 per cent said Ms Sturgeon would get the best deal for Scotland compared to just 13 per cent for former leader Mr Salmond.
More than a third of people surveyed (35 per cent) said they would prefer a Labour government while 16 per cent voiced support for a Conservative government.
Nearly half of SNP voters (48 per cent) said they would prefer a Labour government, with 25 per cent said they would like to see a Labour-led coalition.
Tom Costley, head of TNS Scotland, said: “Nicola Sturgeon and the SNP appear to be going from strength to strength.
“With more people saying they are definitely going to vote than is the case elsewhere in Britain, it suggests that the Scots are more engaged following the independence referendum.
“It remains to be seen what impact the 29 per cent who claim to be undecided as to which way to vote will have on the total number of Westminster seats gained by the SNP.”
SNP campaign director Angus Robertson said: “This poll is yet another welcome indication that the momentum in this campaign continues to be with the SNP - more and more people are putting their trust in the SNP to make Scotland’s voice heard at Westminster, end the cuts and stand up for progressive politics across the UK.
“What this poll also indicates is that support for the SNP is coming from people who voted No in the referendum as well as those who voted Yes - as people recognise that a group of SNP MPs will make Scotland stronger at Westminster.
“Backing for Jim Murphy and Labour continues to fall, as his desperate campaign continues to misfire and fails to resonate with people in Scotland.
“While this poll is welcome, we are taking absolutely nothing for granted and will continue to work as hard as we can to win the trust of people across Scotland.”