The Deputy First Minister responded to growing public anger over soaring gas and electricity prices by pledging to remove energy-efficiency costs from bills. After energy producers announced price rises as high as 9%, Ms Sturgeon said the policy would reduce average bills by 5%.
She told the SNP conference in Perth: "Tackling fuel poverty is one area where we could do so much better with the powers of independence."
The announcement follows Labour leader Ed Miliband's pledge to freeze fuel bills for 20 months, prior to reforming the energy market, if his party wins power in the 2015 UK General Election.
Under the SNP's plan, bills would be reduced by removing an obligation on utility companies to fund energy-saving schemes such as free insulation for some homes, a cost passed on to consumers.
The Scottish Government, which provides an £80 million subsidy for such schemes, would pick up the full £200m cost.
Perth-based energy giant SSE has announced energy prices are to rise on average by 8.2%. British Gas said its prices would increase by an average of 9.2%.
An SNP spokesman insisted the change would not require tax rises as an independent Scotland would qualify for specific green funding from the EU. Better Together, the pro-UK campaign, said the pledge did not "stack up".
Ms Sturgeon promised "not a short-term measure, but a real and lasting cut in Scottish energy bills".
She said: "Independence will allow us to tackle fuel poverty much more directly, delivering Scottish solutions to Scottish problems. Money will be spent in a fully joined-up way on schemes designed in Scotland to meet Scottish circumstances. And this won't just allow us to deliver our energy-saving schemes more effectively, it will also save hard-pressed consumers money."
Tom Greatrex, Scottish Labour's energy spokesman, said: "This looks like a panicked response to Labour's ambitious plans to reset the energy market and another referendum promise it can't deliver. Rather than taking on the big energy firms who are profiteering by ripping off Scottish families, Nicola Sturgeon has come up with a sleight of hand.
"The SNP leadership knows bills would rocket by hundreds of pounds if Scotland separated off and we were left to foot the cost of funding renewables investment, which is currently shared across Britain. Nicola Sturgeon's speech was an admission it has failed to make a coherent case for separation and instead it has resorted to throwing out desperate bribes it can't make good."
Liberal Democrat Energy Secretary Ed Davey has said customers should deal with rising energy bills by using home insulation, adding: "I am sure people wear jumpers. I wear jumpers at home."
Downing Street added yesterday: "If people are giving that advice, that is something they may wish to consider."
Labour leader Ed Miliband said the Conservatives' previous crime policy was to "hug a hoodie", adding "Now their energy policy appears to be "wear a hoodie".
Ms Sturgeon's pledge came in a speech to supporters in which she stressed the SNP's key conference message that Scotland could and should choose independence.
The Deputy First Minister also used her address to announce an extension to the Scottish Government's £20m fund to help mitigate the impact of the so-called bedroom tax, the cut to housing benefit for 80,000 Scots tenants deemed to have surplus rooms.
The cash will be made available in the next financial year. Labour welcomed the move.