Blair Jenkins, chief executive of Yes Scotland, said Alistair Darling had failed to make a positive case for the Union, but Better Together insisted Alex Salmond had failed to answer basic questions for voters.
Mr Jenkins said: "This was a clear win for the Yes campaign - a positive, optimistic and visionary case presented by the First Minister against another dose of negativity and scaremongering from Mr Darling.
"What Mr Darling presented was the No campaign's bankrupt vision for the future of Scotland.
"He not only failed to make a positive case for a No vote - he didn't even try.
"The First Minister presented the positive, compelling case for Scotland taking our future into our own hands and using our vast wealth, talent and resources to build a better and fairer country."
Blair McDougall, chief executive of Better Together, claimed people were turning against the First Minister and his case.
He said: "Tonight's debate will prove to be a huge, possibly decisive, moment in the referendum campaign.
"Alistair Darling asked the questions Scotland needed answers to. The First Minister's failure to offer basic answers was there for all to see. Even the audience was turning against him as time went on.
"Alistair gave a strong performance but what matters more is that we believe his case will prove more persuasive with the remaining undecided voters.
Yes campaigner Pat Kane said he was overall "generally disappointed" with the debate.
He said: "Not much was taken forward because we had two shouty male economists arguing facts and analysis.
"It would be better if these two men on the centre left were working together to solve our problems."
Mr Kane said there was more to the Yes campaign than what was presented by the First Minister during the debate.
John Boyle, the former Motherwell chairman and Better Together supporter, said: "As a businessman I want to know about pounds, shillings and pence and tonight Alex Salmond demonstrated the fundamental flaws in the case for independence. We need to know what currency we are using."
SNP sources said the First Minister was appealing to women voters who did not want to hear a shouting match and the calm approach taken by Mr Salmond would ensure the arguments on welfare and creating a fairer society would win though.
Bookmakers said the debate had not changed the odds on the outcome of the referendum, with No still 1/6 favourite and Yes at 7/2.