When asked who won Tuesday's debate between the Better Together leader and the First Minister, 53% opted for Mr Darling, while 28% backed Alex Salmond as the winner and 19% did not know.
Half of those polled said Scotland should stay in the UK, while 37% backed a Yes vote and the remaining 13% said they did not know.
The Survation poll questioned 1,010 people on August 6 and 7 - two days after the live debate aired on STV.
The majority of people - 65% - said the television clash had not changed the way they intend to vote, while 22% said they were more likely to vote No, and 13% were more likely to vote Yes.
Those polled were also asked about their opinions on alternative plans for currency, the issue which has dominated the referendum debate in the wake of Mr Darling and Mr Salmond's appearance.
Asked if the Scottish Government should draw up alternative currency options to a "currency union" ahead of the referendum, 69% said yes, 18% said no and 13% said they did not know.
Better Together campaign director Blair McDougall said: "This is a bad finish to what has already been the worst week of the campaign so far for Alex Salmond.
"The reason Alex Salmond lost the debate with Alistair Darling wasn't just about style, it was about substance.
"Mr Salmond cannot answer the most basic question about independence: what money would our wages, pensions and benefits be paid in?
"The fact that so many people consider currency to be an important issue underlines how fundamental it is to the whole debate."
A spokesman for Yes Scotland said: "The polls will always fluctuate, but what they all show is that support for Yes is well above 40% - and we are very confident our positive message that a Yes vote is Scotland's one opportunity to protect the NHS, create more jobs here and guarantee that Scotland no longer gets landed with Tory governments we reject, will win a majority on September 18."
The poll comes as the debate over the future currency of an independent Scotland intensified.
Alex Salmond insisted a currency union with the rest of the UK will be agreed, while the main parties at Westminster have ruled this out.
The First Minister said Scotland cannot be stopped from using the pound, and a refusal to share assets such as the Bank of England would mean Scotland could not be expected to take on a share of liabilities such as the national debt.
SNP Treasury spokesperson Stewart Hosie said 57% of people polled support Scotland keeping the pound in the event of a Yes vote.
He said: "As leading economist Anton Muscatelli stated it would be "economic vandalism" for any UK government to turn down a currency union and volunteer to take on an extra £120 billion of debt leaving Scotland without any obligations.
"Taxpayers in the rest of the UK will simply not accept making £5 billion of extra debt payments each year, when Scotland could be paying those debts as part of a currency union. This is a ridiculous position for the anti-independence parties to take."