During a speech at St Andrews University, she told her audience voters did not need to back the SNP to support independence.
She stated that anecdotal evidence suggested there was already a pronounced movement away from a no vote among traditional Labour supporters.
During a speech to an audience composed of members of the public, university academics and staff, she argued that the "transformational potential of independence" was the over-riding reason to vote yes on September 18.
She added: "It should be a reason to vote yes, regardless of what party you vote for. We all want Scotland to succeed. No party has a monopoly on that ambition.
"If you accept the principle that the best way of ensuring success is to give ourselves the powers that help determine it then it doesn't matter whether or not you support the SNP or our specific plans for using those powers."
Speaking after her speech and a question-and-answer session with the audience, Ms Sturgeon said there had already been a significant move towards yes from non-SNP voters.
She said: "We do want to see Labour voters vote Yes. I think it is a section of population where we are starting to see significant movement towards the Yes campaign.
"I've spent a lot of my political life talking to Labour voters and that is where I see the start of quite a pronounced movement from No. Sometimes from No to undecided in the first instance, but sometimes to yes."
Ms Sturgeon also used her speech to highlight the European elections in May, and the importance of the issue of immigration.
She said Scotland could not afford "the narrow-minded approach of the Tories and UKIP on these issues".
She said in her speech: "We are and should remain enthusiastic members of the EU because it is in our national interests to do so.
"Jobs, exports and investment depend on it. Scotland in the EU is the only rational choice for our country but we should be under no illusion about the threat Tory dogma - driven by the electoral threat of Ukip - poses to Scottish interests.
"Similarly, on immigration, our national interests demand a different approach to the one taken by Westminster parties. Our demographics mean that for Scotland sensible migration is an opportunity, not a threat."
A Better Together spokesman said: "The SNP are the ones saying that we should take the risky step of leaving the UK, however they cannot even answer the most basic questions like what currency we would use if we go it alone. People understand that devolution inside the UK works for Scotland. We have the best of both worlds.
"Our Scottish Parliament allows us to make decisions on the areas that matter most like health, education and childcare, and we get the strength and security of being part of one of the world's biggest economies. Why should we trade the success of devolution for the risk and uncertainty of independence?"