During a speech at St Andrews University, Ms Sturgeon told her audience that 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.
"And it should be a reason to vote yes, regardless of what party you vote for," Ms Sturgeon said.
She continued: "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."
She added: "Party loyalty should not be a decisive factor in this debate.
"Indeed, I would have thought that for most Tory voters the idea of a parliament that has the power not just to spend money but also responsibility to raise it and be accountable for how it does so, would be inherently appealing."
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.
"We do want to see Labour voters vote yes," Ms Sturgeon said.
"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."
She said that while persuading Labour voters was not "an exclusive focus" of the yes campaign as the referendum approaches, "arthimetic and the political shape of Scotland would determine that we would want to convince traditional Labour supporters to vote yes".
Ms Sturgeon said: "The argument that is very powerful with Labour voters is the argument of making sure that we have the ability in Scotland to have the kind of economy and society that we want to have, and not one that is determined by Tory governments that we don't vote for.
"That is hugely powerful for Labour."
She added: "I struggle to understand why a Labour politician would prefer to have a Tory prime minister in Downing Street than have a Labour prime minister in Edinburgh."
Ms Sturgeon also used her speech to highlight the European elections in May, and the importance of the issue of immigration.