New polling from Opinium found 53 per cent would choose the SNP for a constituency MSP, up seven per cent from last month.
The Conservatives were on 21 per cent, Labour 18 per cent and the Liberal Democrats on 6 per cent.
In the regional vote, 44 per cent chose the SNP, the Conservatives were unchanged on 22 per cent, Labour were on 17 per cent while Alba registered just 2 per cent.
If these results are translated roughly into seats, it would see the SNP enjoy a majority in the Scottish Parliament of 13.
Conducted the Sky, the polling interviewed 1,023 Scottish adults online between April 1 and April 6.
The SNP would have 71 seats, while the Conservatives would be on 27 seats, Labour on 21, the Greens on 6 and Lib Dems on 4.
Alex Salmond's new Alba Party would be unlikely to land a single seat.
Just 11 per cent think Alex Salmond mainly has Scotland’s best interests at heart, while 65 per cent think he has his own
Voters responded negatively towards Mr Salmond’s “supermajority” pitch, with 63 per cent thinking an Alba and SNO coalition would be bad.
This compares to a coalition between the SNP and the Greens which 41 per cent think would be good.
The polling has not translated into a boost for independence however, which remains on 51 per cent when the don’t knows are excluded.
Chris Curtis, Senior Research Manager at Opinium, comments: “If Scottish unionists had been hoping that the fallout between Salmond and Sturgeon would hurt the SNP, then our latest polling is going to be a disappointment. It looks like being on the campaign trail has further boosted the First Minister’s ratings, while the unpopularity of Alex Salmond has meant he is struggling to make a dent.
“Perhaps the most disappointing results in the poll are for the Labour party. Their new leader’s surging popularity is currently failing to translate into any more votes, as Labour ends up in the unenviable position of being everyone’s second choice.”