In 90 minutes of questioning - the closest the two candidates will get to debates after May's refusal to share the stage with Corbyn - Brexit took a back seat even though it was what the British prime minister cited as her reason for calling the election three years earlier than was required.
Addressing activists, Mrs May warned that the party only had to lose six seats in the election for its Commons majority to disappear, opening the way to Downing Street for Labour.
However, another audience member wasn't as polite about May's views.
She was more confident on Brexit, winning applause when she repeated that no deal was better than a bad deal on leaving the EU.
Mr Corbyn replied: "We got along absolutely fine".
He would not be drawn on whether he would order a drone strike strike against a terrorist plotting overseas to attack the UK.
But Paxman set the tone by saying that if he were an European Union negotiator who had observed all her recent flip flops, he would think of her as a "blowhard who collapses at the first sound of gunfire".
Following the refusal by Prime Minister Theresa May to face her rivals in a televised debate, the Sky News-Channel 4 co-hosted show saw Mrs May and Labour leader Jeremy Corbyn responding to questions from the audience and interviewer Jeremy Paxman instead.
He escaped mostly unscathed, most notably when Mr Paxman asked him why his longstanding wish to abolish the monarchy was not in the Labour manifesto.
"Look, there's nothing in there as we're not going to do it", said Mr Corbyn, who is known for his republican beliefs.
Ms Rudd also claimed Mrs May had "levelled with people" about the social care reforms.
Ms Barnett said: "I presume you have the figures?"
The pair's appearance on the Sky News/Channel 4 "Battle for Number 10" broadcast is trending on Twitter with popular hashtags including #BattleForNumber10 and #mayvcorbyn, while thousands of tweets made reference to the programme's hosts Jeremy Paxman and Faisal Islam.
May often found herself on the defensive as audience members grilled her on cuts to the police, National Health Service and education, and a so-called "dementia tax" that might make it harder for elderly Britons to pass on their property to their heirs.
The Prime Minister argued that counter-terrorism budgets had been protected and said more money was being used to target new threats such as cyber-crime.