The Ipsos-Mori poll for the London Evening Standard found 53% of voters planned to vote No, while 47% said they would vote Yes, after excluding undecided voters.
About 4% of the 991 people questioned still had to make up their minds how to vote, according to the poll carried out on Tuesday and Wednesday.
The study echoes other recent opinion polls which gave the pro-unionists a narrow lead.
A YouGov survey for The Sun and The Times found 52% of Scots were to vote for the union with 48% favouring independence, when undecided voters were excluded.
The result was mirrored in a Panelbase survey which also found 52% of Scots backed the union compared with 48% for independence, again with undecided voters excluded.
A survey by Ipsos-Mori for the broadcaster STV suggested the gap could be even closer.
It found 51% of people were voting No, with 49% backing Yes, when undecided voters were excluded.
When those who were yet to make up their minds were factored in, the No campaign was on about 49%, Yes on 47% and 5% said they did not know how they would cast their ballot.
The latest YouGov result remained unchanged from the last poll conducted six days ago.
It excluded the “don’t knows” who made up 6% of the survey.
It said its research also suggested men were more likely to vote for independence by a margin of 54% to 46%, while women would prefer Scotland to remain in the UK by a margin of 57% to 43%.
YouGov said the result was compiled after 3,237 electors were questioned between Monday and Wednesday.
The Panelbase survey came out less that 24 hours before voting got under way in the referendum and was another indication that the campaign over the future of the UK could go down to the wire.
Exactly half of the 1,004 people questioned said they would be voting No to independence, with 45% voting Yes.
Just one in 20 (5%) of voters still had to make up their mind, according to the research.
It added that men continued to be more likely to support Scotland leaving the UK, with about 54% said to be Yes voters, 44% who were voting No and 3% who were undecided.
Just under two-fifths (39%) of women questioned said they would be voting Yes, with 54% backing No and 7% still undecided.
Survation also released its final poll on the referendum, which suggested 53% of voters would support Scotland remaining in the union while 47% would vote Yes, when undecided electors are excluded.
When the 9% of those unsure how they were voting were included, the No campaign received 48% while Yes picked up 43%.
The poll for the Daily Record was conducted by telephone over a 24-hour period on Tuesday and Wednesday.
Survation said the poll reached 1,266 respondents but had an effective sample size of 1,089.