The senior Tory was quizzed by moderator Mishal Husain over why the policy document was not fully costed. "Judge us on our record," Rudd declared, with some members of the public bursting into laughter.
The seven-way debate, including Ukip leader Paul Nuttall and Green co-leader Caroline Lucas, comes just over a week before the general election on 8 June.
But Prime Minister Theresa May has refused to take part in the TV event. Labour leader Jeremy Corbyn had said he would not participate in such debates unless May was present. However, the left-winger dramatically U-turn on the vow and took part in the BBC debate.
Liberal Democrat leader Tim Farron, meanwhile, took the opportunity to attack May over the so called "dementia tax".
The Conservative policy would see elderly voters in England with more than £100,000 in assets have to pay for their social care costs.
"Where do you think Theresa May is tonight?" Farron said. "Take a look out your window. She might be out there sizing up your house to pay for your social care."
The latest poll from Kantar, of more than 1,000 people 25 and 30 May, put the Tories 10 points ahead of Labour (43% versus 33%), with the Liberal Democrats on 11% and both Ukip and the SNP on 4%.