The ex-Chancellor said he is prepared to dig out up to £10billion to soften the impact of October's price rise.
And the plan to scrap VAT on energy will reduce bills for every household by £200.
His comments come as a direct challenge to Tory leadership rival Liz Truss, who so far has only committed to "considering" the measure.
She told a GB News audience in Leigh this week that she can "put spades in the ground" and deliver on jobs as she laid out her tax-cutting credentials to tackle the cost-of-living crisis.
Mr Sunak, outlining a very different approach, says he would find up to £5billion more to help those most vulnerable to rising prices while accepting that his VAT plan would cost an additional £5billion.
Rishi Sunak is hoping to be the country's next PM
Ben Birchall
Liz Truss during a campaign visit to a life sciences laboratory at Alderley Park, Manchester
Christopher Furlong
In an article for The Times, he said: “People need reassurance now about what we will do and I make no apology for concentrating on what matters most.
“Whatever the ‘boosterish’ talk of others, you can’t heat your home with hope.”
The 42-year-old will offer specific support to pensioners and those on benefits as they “simply cannot increase their incomes to meet their energy costs and are the most vulnerable in society”.
Universal Credit and winter fuel payments will be used to top up their incomes.
Ms Truss, meanwhile, has defended earnings at energy companies as she insisted profits should not be considered "dirty and evil".
She said windfall taxes on profits are more about "bashing business" than achieving real results.
The 47-year-old added: "I don't think profit is a dirty word, and the fact it's become a dirty word in our society is a massive problem.
"Now, of course, the energy giants, if they're in an oligopoly, should be held to account, and I would make sure they're rigorously held to account.
"But the way we bandy the word around 'profit' as if it's something that's dirty and evil, we shouldn't be doing that as Conservatives."
It comes as the energy crisis appears to take over the leadership discourse.
On Thursday, outgoing Prime Minister Boris Johnson met with energy bosses as he appealed for their help to ease the pressure on families.
Ms Truss and Mr Sunak are both under pressure to meet with the PM to address the cost-of-living row more urgently.
The winner of the Conservative Party leadership race will take up residence in Downing Street by early September.