Watch: Rishi Sunak accused of ‘mansplaining’ after interrupting Liz Truss multiple times
The former chancellor and the foreign secretary were quizzed on the BBC's Our Next Prime Minister: The Build Up on Monday night.
The show quickly turned bitter as the pair debated the economy, where they clashed over taxation.
As Truss was questioned about her policies on tax, Sunak repeatedly cut across her.
Sunak's behaviour swiftly triggered a backlash - with accusations the former chancellor was "mansplaining".
"Rishi Sunak has tonight proven he is not fit for office," a spokesperson for Truss told The Times.
"His aggressive mansplaining and shouty private school behaviour is desperate, unbecoming and is a gift to Labour."
Immediate polling after the debate indicated Sunak's performance had not gone down well, with one Opinium poll of Conservative voters showing they believed Truss did better (47% vs 38% for Sunak).
Tory MP Jackie Doyle-Price also criticised Sunak.
"Most women MPs have been subject to mansplaining and being talked over in debate," said Doyle-Price. "Never a worse example than right now on the BBC."
Sunak even tweeted a clip from the debate - in which he branded Truss's proposed £40bn tax cuts as "unfunded and irresponsible - which showed him talking over his rival.
During the debate, a visibly frustrated Sunak said Truss would pay for her promised tax cuts by putting it "on the country's credit card".
He said that to do that was "un-Conservative" and would burden future generations with debt.
The former chancellor has ruled out immediate tax cuts claiming they will stoke inflation.
Truss rejected claims she was burdening future generations with debt and suggested her plans were responsible.
“Rishi, that is not true," said Truss.
"Under my plans, we would start paying down the debts in three years time. COVID was a one in 100 years event, no other country is putting up taxes at this moment.
"The OECD has described Rishi’s policies as contractionary.”
Truss has argued that tax cuts are needed to help those struggling with the cost-of-living and to boost economic growth.
Following the televised debate, Sunak's allies praised his performance.
Tory MP George Freeman said: "Tonight’s BBC Our Next PM debate illustrated why I think Rishi Sunak is the right person to be our next Conservatives Leader and Prime Minister."
Freeman said Sunak demonstrates qualities like "eloquence" and "decency" during the show.
Despite the tense exchanges, Truss and Sunak did find some kind words for each other at the end of the debate.
The foreign secretary praised Sunak's dress sense, and said she would want to work with Sunak while in government.
"It's been fantastic working with you," said Truss to Sunak.
"We've always got on well, and I think we have shared a belief in Britain."
And the former chancellor said Truss "deserves huge credit for being a big part of standing up to Russia" since Vladimir Putin's invasion of Ukraine.
"Over the last six months she's worked with me, with foreign ministers across the world, to ensure we had a very robust response [to Putin].
"I saw her and her best doing that, and there is far more that unites us than that we disagree on."
Watch: Key moments from the BBC’s Tory leadership debate