The Scottish First Minister and the former chancellor, who is leading the Better Together campaign to keep Scotland in the UK, faced each other for the first time in a TV debate last night.
With just six weeks to go until voters north of the border decide if Scotland remains in the UK in the September 18 referendum, the debate between the rival politicians saw heated clashes over issues such as what the currency of an independent Scotland would be.
A snap poll by ICM for The Guardian newspaper indicated Mr Darling may have scored a narrow victory over the SNP leader, winning the debate by 56% to 44%.
Broadcaster STV, which screened the clash, said it had attracted 1.7 million viewers, including 500,000 who watched the debate online.
Mr Salmond said the ICM poll had found an increase in support for independence, saying: "The Yes support, people watching the debate, started at 45% which is high, and went up to 47%, which is in touching distance of victory.
"Particularly significant is the surge in support from women, and the fact that I think 74% of undecided voters thought the Yes side won the debate. These are great findings for us, they show we are pursuing the right strategy."
He added: "There is six weeks of this campaign. I think everybody knows now that we are in a real position of possible victory.
"We are the underdogs, I relish that position."
He said Mr Darling resorted to being "shouty man" in the TV debate, and added: "I am absolutely certain that the way to not just win this campaign, but to win the hearts and minds of the people, is to have a discussion.
"Not to shout at them, not to point your finger at them, not to wave your hands about, but to actually have a conversation about what matters to people and their families."
But Mr Darling said the First Minister has failed to come up with the answers needed on issues such as what currency an independent Scotland would use if it could not agree a deal with the rest of the UK to keep the pound.
The Better Together leader said: "I think it was a good debate, but the important thing is Scotland wants to know the answer on what currency we will use.
"Alex Salmond, despite being asked time and again, couldn't answer that basic question. We don't know what his plan B is, and with six weeks to go that is not good enough.
"You can't rely on guesswork, fingers crossed, we need to know what his plan B is and he won't tell us.
"In a debate you're supposed to come up with answers. Now, he had the odd good line but he had no answer.
"Scotland wants to know that and he couldn't come up with an answer. Scotland wants to know what plan B is.
"He's got six weeks to do it. The fact that he hasn't got one now is frankly incredible, which is why he came off the worst."
The former chancellor added: "The only thing I want to win is the referendum in six weeks' time.
"I think we will win if we continue to get our arguments across, and we will win for as long as the nationalists can't answer basic questions - of which the currency is the most basic."
But Mr Salmond again insisted Scotland would continue to use the pound if it left the UK.
In the debate, when pressed on the matter by Mr Darling, the First Minister said Scotland would keep the pound "because it belongs to Scotland as much as it belongs to England".
Today the SNP leader said: "Nobody can be in any doubt that the Scottish Government's policy is to keep the pound.
"Why? Because it is our pound, it is not (Chancellor) George Osborne's, it is not Alistair Darling's, we can't be dictated to. It is part of the assets of the country to which we are entitled to keep, if the sovereign will of the Scottish people in a referendum says that is what we do, then that is what will happen."
But polling expert Professor John Curtice, from Strathclyde University, said there was no clear winner in the debate, adding both men had failed to convince undecided voters to back their side.
He told BBC Radio Scotland: "The evidence of the ICM poll is that for the most part Yes supporters thought Alex Salmond had won, No supporters for the most part thought Alistair Darling won.
"The undecided were fairly evenly divided, with maybe a slight edge for Mr Salmond. That suggests, frankly, neither side secured a decisive advantage."