The survey also shows a narrow lead for Yes after recent trends showed support for the union had pulled ahead.
However, this is Opinium’s first poll in Scotland since the 2019 general election, meaning the numbers are not directly comparable to other pollster’s estimates for both Holyrood and indyref2.
The poll interviewed 1,096 Scottish adults aged 16+ online between March 11 and 16.
It puts support for the SNP at 46 per cent in the constituency vote and 42 per cent on the regional list with the Scottish Conservatives their closest challengers on 24 per cent and 22 per cent respectively.
Labour are holding on to third place on both ballots with 20 per cent for constituencies and 19 per cent on the regional list.
The Liberal Democrats are set for six per cent on the constituency ballot and five per cent on the regional list, close to the Greens who are polling at four and seven per cent respectively.
Opinium said such a result would see the SNP miss out on a majority in Holyrood by one seat, the Tories lose two seats to 29, Labour unchanged on 24, and the Greens up one seat to seven, with the Liberal Democrats taking the rest.
On independence, Opinium said support for a potential Yes vote would see 51 per cent of Scotland vote in favour of leaving the UK, with 49 per cent voting No.
The pollsters did not provide a voting intention which included don’t knows.
Chris Curtis, senior research manager at Opinium, said: “The polling shows the future of Scotland rests on a knife edge. Firstly, in terms of whether the SNP can gain a majority alone in May, which would strengthen their mandate to hold a second independence referendum. Secondly, in terms of what might happen in such a referendum, with “Yes” and “No” eye wateringly close in our latest poll.
"But it is also important to note Sturgeon’s incredible popularity in Scotland. Despite her recent difficulties over the Salmond affair, she still has the overwhelming support of Scottish voters, driven by the fact that most think her government has done a good job responding to the pandemic.”