It found 51 per cent of people are voting No, with 49 per cent backing Yes, when undecided voters are excluded.
When those who are yet to make up their mind are factored in, the No campaign is on 49 per cent, Yes on 47 per cent and 5 per cent said they do not know how they will cast their ballot.
Blair Jenkins, Yes Scotland chief executive, said the Ipsos-MORI poll showed a seven-point rise in support for independence within the last month, adding that support for the union had fallen by the same amount over the period.
Mr Jenkins said: “This is hugely encouraging, and demonstrates that Yes has the momentum as we go into referendum day - with a seven-point surge since last month.
“This poll - like all the recent polls - show that we are in touching distance of success. The referendum is on a knife edge, and this will spur on everybody who wants and is working hard for a Yes to redouble their efforts.”
Mark Diffley, director at Ipsos MORI Scotland, said: “With hours to go now until the polls open, it is clear that the result of the independence referendum is extremely close.
“Yes have made significant gains in recent week, to such an extent that the outcome is finely balanced. Both campaigns now will be entirely focused on persuading undecided voters and on ensuring that their supporters turn out to vote tomorrow.”
Better Together campaign director Blair McDougall responded: “No-one today can afford a protest vote. If we vote to leave the UK there would be no going back, no matter the risks to our jobs, pensions and NHS.
“There are so many unanswered questions in this referendum. If you don’t know, vote No.
“There is a better way to make our country a better place to live. We can have faster, better, safer change for Scotland within the UK. That’s why we should vote No.”