A new Ipsos MORI poll for showed a rise in support for the Yes campaign, while support for the UK is unchanged.
Among those who described themselves as being "certain to vote" in the referendum, 40% said they supported independence, an increase of four percentage points from June.
Meanwhile the proportion of people who favour Scotland staying part of the UK remained static at 54%. Just 6% of those polled said they had not yet decided how they would vote, down from 10% in June.
A total of 1,006 people in Scotland were questioned between July 28 and August 3 for the research.
When the undecided voters were factored out, the poll put support for the UK at 58%, a drop of two percentage points from June, while support for independence was up by two points to 42%.
Of those who were surveyed, 81% said they were "absolutely certain" to vote in the referendum, including 89% of those aged 55 and above and 59% of young voters in the 16 to 24 age group.
The poll was conducted during the Glasgow 2014 Commonwealth Games, with 96% of people stating that the sporting tournament was either "very successful" or "fairly successful".
But 89% of people questioned said the sporting tournament would have no impact on how they will cast their ballot in September.
Mark Diffley, director at Ipsos MORI Scotland, said: "With 45 days to go until the referendum the Yes campaign will be heartened that it continues to narrow the gap in public opinion. It appears that the gains made by Yes are driven by undecided voters deciding to vote in favour of independence in September.
"The No campaign will take some comfort that support for the union remains unchanged and that it retains a significant lead with the referendum fast approaching."
He added: "The Commonwealth Games has proved a complete triumph with the public though it appears to have had little effect on voting intentions in September."