She drew on calculations that the country could have expected an extra £850 million in funds through the common agricultural policy, leading to a £1 billion economic boost between this year and 2020.
The claim was central to the SNP deputy's speech to the David Hume Institute in Edinburgh, which has embarked on a series of forums putting each Holyrood party leader in the spotlight on independence.
As well as claiming additional EU benefits as a consequence of a yes vote in September, Ms Sturgeon said her opponents will come round to a "common sense" position on continued Scottish membership as a state in its own right.
The same applies to the Scottish Government's plan to share the pound as currency - a position doubted by senior unionists and some academics in the UK and wider Europe.
Stating the case for independence, she asked why people would want to defer decision-making to "others" in the UK Government.
"In an independent Scotland the government, of whatever colour, will always put the interests of Scotland first," she told an audience at the Royal Society of Edinburgh.
"The current Scottish Government believes those interests lie in being a full member of the European Union. Today, we have published research showing that if we were an independent member state we would benefit from an extra £850 million in common agricultural policy funding.
"That money would support an additional 2,500 jobs and increase economic output by £1 billion."
She rejected claims that Scotland would be forced out of the EU during negotiations.
Ms Sturgeon said common sense will prevail on other Scottish Government policy aims.
It follows a Treasury announcement that it will honour all UK Government debt up to the date of potential Scottish independence.
"The barriers the No campaign have sought to build all fall down when faced with simple logic and common sense," she said.
Ms Sturgeon faced questions from the audience on the contents of the Scottish Government's blueprint for independence, including the suggestion that Nationalists appear only to see positives in the debate on the constitutional future.
Asked to concede any "minus" point about independence, she said: "There is a big minus. We'll have nobody else to blame. I wouldn't be able to stand here and blame the Westminster government for anything that went wrong."
But the big worry for her is that the opportunity for independence may not come again.
"What worries me about how we sometimes, perhaps, seem as if we're articulating our argument, is that independence makes us immune from challenges in the future - it doesn't," she said.
"We face big challenges just like other countries do. We will no doubt, like every other country, have rocky periods. We'll have times when things don't go right.
"These are things that worry politicians and governments in any country.
"But I cannot for the life of me think of the situation in which it would be better to leave responsibility elsewhere than to have responsibility for navigating your way through these things and finding solutions for ourselves.
"Genuinely what worries me more than anything at the moment is that we don't take this opportunity because we genuinely might not get it again."