The main opposition party is level with the Nationalists at 38% for the constituency vote but three points clear in the regional top-up vote at 37%, according to the YouGov poll in The Times.
Translated into seats, it could make Labour the largest party at Holyrood, but still short of the SNP's historic absolute majority in the 2011 election.
The next election is not until 2016, beyond the independence referendum in September 2014.
The survey indicates a marked shift from May 2011 when the SNP won 69 seats and formed a majority government after four years in a minority administration.
Labour was heavily defeated then, moving from 46 seats to 37 in the 129-seat parliament.
Despite Labour's improved rating, the poll also shows a strengthening SNP vote, moving up one point in constituencies and regions more than six years after taking power.
Labour support increased by four points in constituency voting intentions and by six points in regions.
Support for the Conservatives slipped two points to 14% in constituencies and by one point down to 14 in the regions.
The Liberal Democrats remain at 5% in constituencies and dropped one point to 5% in regions.
Support for the Greens dropped from 7% to just 3% in the regional vote - level with Ukip and the Socialist Party.
The figures are compared to a previous YouGov poll from September. Polls usually have a +/-3% margin of error.
A spokesman for the SNP said: "After over six-and-a-half years in government, it is very encouraging to see SNP support increasing in both the constituency and list votes, and another poll published this week showed a continued lead for the SNP.
"At this stage in the last Scottish parliament, a YouGov poll had Labour ahead in both the constituency and list votes - so they are actually in a relatively worse position in this parliament - and the SNP went on to achieve a fantastic win in the 2011 election."