The parties are neck-and-neck in the second, regional, vote list conducted under the Scottish electoral system.
Labour were down two points on the comparable last poll, conducted in October, while the Tories were up one.
The margin of error means the parties are effectively neck-and-neck overall.
The snapshot however represents a huge turnaround for the parties, with Labour having run the Scottish Government in coalition as recently as 2007.
The Conservatives have by contrast been completely panned by Scottish voters since the 1997, where they lost all their Westminster seats.
The Scottish National Party lead the pack with 51 per cent of the constituency vote and 42 per cent of the list vote.
The Lib Dems are on five per cent while the Green Party is on six percent on the list vote only.
Scotland goes to the polls
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The poll comes as Scottish Labour leader Kezia Dugdale announced a plan to raise income tax by one per cent to raise £500m to protect public services from Westminster cuts.
The SNP and the Tories rejected the move and said it would punish Scotland’s low-paid workers, but Labour said a rebate could be provided to people on low incomes.
As recently as 2015 Labour had 41 Westminster seats in Scotland. It however lost all but one under the leadership of Jim Murphy and Ed Miliband.
An internal report by the party into its defeat found that it was seen as "indistinguishable from the Tories" in Scotland after campaigning alongside them at the 2014 independence referendum.
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