The TNS survey, conducted during the Commonwealth Games and following last week's TV debate between Alex Salmond and Alistair Darling, put support for No on 45 per cent, up four points compared with the previous month and the highest since the company's regular run of polls began last September.
Backing for Yes remained unchanged on 32 per cent, while 23 per cent of voters remained undecided, down four points.
However, among the 71 per cent of voters who said they were certain to vote on September 18, backing for Yes rose a point to 38 per cent, its highest level since September.
Support for No remained unchanged on 46 per cent while the don't-knows fell to 16 per cent.
Both sides welcomed the findings yesterday.
Claiming the momentum was with the No camp, Better Together campaign director Blair McDougall said: "Alex Salmond had the chance to be honest with people about Scotland, about the risks of independence, but he failed to do so.
"It's no wonder Scots are rejecting separation when we don't know what money our wages, pensions or benefits would be paid in if we left the UK.
"Alex Salmond can't expect us to take a leap in the dark on the basis of his blind faith."
Better Together closed its online appeal for donations yesterday and said it was no longer seeking campaign funding after a flurry of small gifts following last week's TV debate, which saw Mr Salmond refuse repeatedly to outline his preferred alternative to sharing the pound with the UK, a proposal publicly ruled out by the Conservative-Lib Dem Government and Labour opposition.
Yes Scotland chief executive Blair Jenkins said: "These are encouraging findings.
"Among those in the TNS poll who are certain to vote, the gap has narrowed further this month, putting Yes at a new high.
"Once don't knows are excluded, Yes is at 45 per cent, and two other recent polls put Yes support as high as 47 per cent -within touching distance of a majority in September."
Today's TNS poll also showed large numbers of people feel unsure about what would follow either a Yes or No vote.
Fewer than one in three (29 per cent) said they had enough information about what would happen if Scotland became independent. Slightly more (36 per cent) said they had enough information about what would follow a No vote.
Tom Costley, head of TNS Scotland, said: "The fact that opinion among those certain to vote is holding steady is consistent with our previous polling, which has shown voters on both sides are firmly committed to their views.
"With only a few weeks until the referendum, the hopes of the Yes campaign rest on winning over most of the dwindling number of undecided voters. At the end of last year, 25 per cent of those who said they were certain to vote had not made up their minds: that important pool of voters is now a third smaller."
He added: "While it would appear that there is still a lot of uncertainty about what will follow a Yes vote, the lack of clarity about a No vote suggests many are still unsure about the additional powers being offered to Scotland by the main unionist parties."
The result of the poll of 1003 over-16s, conducted between July 23 and August 7, came as jobs dominated the day's campaigning.
With 35 days to go, Finance Secretary John Swinney unveiled an action plan to create full employment in an independent Scotland.