It came as not one of the candidates to replace Boris Johnson said they would be willing to have him in their Cabinet.
In a sometimes bad-tempered debate, the former chancellor accused Foreign Secretary Liz Truss of peddling “something-for-nothing” economics after she said he was choking off growth by raising taxes to their highest level in 70 years.
And after Penny Mordaunt, the international trade minister, said she would not keep to his rule of only borrowing to invest, Mr Sunak said even former Labour leader Jeremy Corbyn did not advocate such a fiscal loosening.
Another round of voting by Tory MPs is due to take place on Monday, with the candidate who comes last kicked out of the contest.
The five hopefuls – Mr Sunak, Ms Truss, Ms Mordaunt, Kemi Badenoch and Tom Tugendhat – will be whittled down to two in the coming days, before Tory Party members pick the next prime minister in a postal ballot.
Mr Sunak, who currently boasts the most support among Tory MPs, came under sustained fire in the second TV debate, with Ms Truss attacking his record in the Treasury.
She said: “Rishi, you have raised taxes to the highest level in 70 years. That is not going to drive economic growth.
“You raised national insurance, even though people like me opposed it in Cabinet at the time because we could have afforded to fund the NHS through general taxation.
“The fact is that raising taxes at this moment will choke off economic growth; it will prevent us getting the revenue we need to pay off the debt.”
The Foreign Secretary has vowed to axe the planned corporation tax hike, reverse the national insurance rise and implement a temporary moratorium on the green energy levy in a multibillion-pound pitch for the Tory leadership,
Mr Sunak said the pandemic damaged the economy and public finances had to be rebuilt.
He added: “I’d love to stand here and say, ‘Look, I’ll cut this tax, that tax and another tax and it will all be OK.’ But you know what? It won’t.
“There’s a cost to these things and the cost of higher inflation, higher mortgage rates, eroded savings. And you know what? This something-for-nothing economics isn’t Conservative. It’s socialism.”
Ms Mordaunt said the limited tax cuts she advocated were not inflationary and people need help now with the cost of living.
“I don’t understand why Rishi doesn’t understand that,” she said.
Mr Sunak hit back: “It is one thing to borrow for long-term investment. It is a whole other thing to put the day-to-day bills on the country’s credit card. It is not just wrong, it is dangerous.
“Even Jeremy Corbyn didn’t go that far.”
He later added: "We've actually got to the point, and we should reflect on this as a Conservative Party, where even [Labour leader] Keir Starmer is attacking leadership candidates for peddling the fantasy economics of unfunded promises.
"If we're not for sound money, what is the point in the Conservative Party?"
The former chancellor and Ms Truss traded further barbs during a section in which the candidates could quiz each other.
Mr Sunak asked the Foreign Secretary: “In your past, you’ve been both a Liberal Democrat and a Remainer. I was just wondering which one you regretted most?”
Ms Truss said she was not born into the Conservative Party and went to a state school, adding: “My fundamental belief and the reason I am a Conservative, is I saw kids at my school being left out in Leeds.
"I saw them not get the opportunities, not get the proper educational standards that you might have got at your school, Rishi.”
Mr Sunak attended the private school Winchester College.
Earlier, the former chancellor sought to underline his Brexit credentials in a stylised social media video which branded him “a real Brexiteer from day one”.
The video said he went against “increasing pressure from his bosses to back Remain”, and took a direct swipe at Ms Truss by pointing out she campaigned to stay in the EU.
Despite voting to Remain, Ms Truss has attracted support from high-profile Brexit-backers and allies of Mr Johnson. She is seeking to unite the right of the party.
There were further bad-tempered exchanges between Ms Mordaunt and Ms Badenoch.
The latter had previously accused Ms Mordaunt of having pushed a policy of gender self-identification for trans people when she had government responsibility for the issue – a controversial issue within the Tory Party.
Following further reports in the press casting doubts on her denials, Ms Mordaunt said: “I know why this is being done but I would say all attempts to paint me as an out of touch individual will fail.”
Ms Badenoch repeatedly tried to interrupt, saying: “Penny, I was just telling the truth. I am telling the truth.”
Ms Truss also denied that she was running a negative campaign following attacks on Mr Sunak by some of her supporters.
In a remarkable moment, when asked to raise their hand if they would be happy to have Mr Johnson in their Cabinet “if he wished to serve”, none of the five candidates did so.
The hopefuls also ruled out a snap election if they won the keys to Downing Street.
Earlier on Sunday, Ms Mordaunt hit out at “toxic politics” and “smears” which she claimed were dragging the leadership contest down.
She told the BBC’s Sunday Morning programme: “There is a number of smears going on in the papers. My colleagues are very angry and upset that this is how the leadership contest is being dragged down.”
She also said there were no circumstances in which she would agree to a second referendum on Scottish independence, insisting the question was “settled”.
Mr Tugendhat said it was a “generational decision” and a “generation hasn’t passed”.
Responding to the second TV debate, SNP deputy Westminster leader Kirsten Oswald said: “Once again, Scotland is lucky to get a cursory mention in a debate where the candidates failed to escape the Westminster bubble for the public at home.
“While the cost of living crisis hits households – and people are terrified to open their bills – the Tories are too busy engaging in a race to the bottom on green energy support and renouncing Boris Johnson despite supporting him consistently over the last three years.
“The candidates need to listen to the public instead of each other - the cost of living crisis must be the immediate priority for the next occupant of Downing Street.”