With less than two weeks to go before the Sept. 18 vote, the poll put the "Yes" to independence campaign on 51 percent against "no" camp on 49 percent, overturning a 22-point lead for the unionist campaign in just a month, the Sunday Times said.
YouGov said that the results excluded those who would not vote and those who did not plan to vote or did not know how they would vote. With those groups included, secessionists would be on 47 percent and those championing the United Kingdom would be on 45 percent, it added.
It said that the poll, conducted after pro-independence leader Alex Salmond was widely judged to have won the second of two televised debates, amounts to a statistical dead heat at the moment. "The last poll ... was the first to represent a real possibility for a "yes" win ...," it said.
A separate poll by Panelbase, commissioned by the pro-independence campaign, showed support for a breakaway rising but still short of a majority at 48 percent. When undecideds were included, that fell to 44 percent.
After months of surveys showing nationalists heading for defeat, recent polls have been showing the gap narrowing to the extent that they raise the real prospect that secessionists led by Salmond's Scottish National Party (SNP) could achieve their goal of breaking the 307-year-old union with England.
A previous YouGov poll on Sept. 1 put the lead for the "no" to secession campaign at just six points, down from 14 points in the middle of August and 22 points at the start of that month.
But the latest average of the polls, issued on Sept. 1 by Strathclyde University Professor of Politics John Curtice, still placed the unionist lead at 10 points.
The late showing by the independence camp has hit sterling on the foreign exchanges and electrified Britain's political class after its summer break.
A vote to break away would be followed by negotiations with London on what to do about the currency, national debt, North Sea oil and the future of Britain's nuclear submarine base in Scotland ahead of independence penciled in for March 24, 2016.
If Scots voted to leave the United Kingdom, Prime Minister David Cameron would face calls to resign before a national election in May 2015 while the opposition Labour party's chances of gaining a majority could be scuppered if it lost its Scottish lawmakers.
Cameron, who was due to visit Queen Elizabeth in Scotland on Sunday, has insisted he will not resign.
Nationalists accuse London of squandering Scottish wealth and say that Scotland would be one of the world's richest countries if it took control of its own destiny.
Unionists, including Britain's three main political parties, say the United Kingdom is stronger if it stays together and that Scottish independence would bring significant financial, economic and political uncertainty.
Politicians from the "Better Together" unionist campaign have been trying to tempt Scots with offers of greater devolution.
This week, former prime minister Gordon Brown, himself a Scot, promised Edinburgh more powers over its tax, social and economic affairs if Scots voted against independence.
The Observer newspaper said British ministers planned to make further concrete offers in coming days to allow Scots to devise a federal future for their country.