Mr Sunak and Ms Truss clashed most ferociously over their Brexit record and their plans for taxation in the UK as they addressed the audience in Hanley's Victoria Hall.
Appearing after the two were selected as the final two candidates by Tory MPs, they attempted to sway voters who backed Prime Minister Boris Johnson in the last election that their path was the right way forward.
Ms Truss was particularly vocal in her criticism of the former Chancellor's taxation plans, saying his policies will crash the economy and that his emphasis on paying back debt is a "massive mistake".
The Foreign Secretary said during the BBC debate: “I would obviously make sure, my Chancellor would make sure that we optimise the way we are taking out those debts.
“The point I am making is, I am illustrating the fact that when you have a major world event, a major economic shock, trying to pay back the debt as quickly as possible is not the right thing to do economically.
“We didn’t do that after World War 2. We shouldn’t do that now.
"And crashing the economy in order to pay a debt back quicker is a massive mistake.”
Rishi Sunak and Liz Truss before taking part in the Tory leadership debate, based in Stoke-on-Trent
Jacob King
Former Chancellor addresses the Stoke-on-Trent crowd
Jacob King
Interjecting, Mr Sunak told the Victoria Hall crowd: “The mistake that we will make is that at a time when inflation is already high, everyone’s already feeling it in their belt, interest rates are already on the rise, so, into that situation does anyone think that the sensible thing to do is go on a massive borrowing spree worth tens of billions of pounds and fuel inflation?”
The former Chancellor said that “if we do, inflation stays here for longer and interest rates are going to go up”.
In response, Ms Truss accused him of fearmongering.
Brexit was also an issue that provoked a strong reaction from the two candidates.
Mr Sunak reminded the Stoke-on-Trent audience that "only one of us was on the Leave campaign" – a particularly potent point given Stoke voted strongly in favour of pulling out of the EU in 2016.
To this, Ms Truss insisted she has changed her mind and is committed to making Brexit a success.
The debate came just hours after a Tory peer claimed Boris Johnson “does not want to resign” and “wished that he could carry on” as Prime Minister.
Lord Cruddas of Shoreditch, a former Conservative Party treasurer, said the comments were made to him by Mr Johnson over lunch at Chequers on Friday.
The peer is running a campaign to give party members a vote on whether to accept Mr Johnson’s resignation as Tory leader.
Downing Street responded by insisting Mr Johnson will leave the post when a new Tory leader is chosen in September.
A Number 10 spokeswoman said: “The Prime Minister has resigned as party leader and set out his intention to stand down as PM when the new leader is in place.”
Both candidates ruled out a job for Mr Johnson in their cabinet, with Ms Truss saying she believes he “needs a well-earned break”.
She added: “I am sure he will have a role, I am sure he will be vocal but he will not be part of the Government.”
Mr Sunak was more direct in his reply by saying: “The simple answer for me is no.”
Initial reaction suggests the debate was a fairly even contest, which arguably favours Ms Truss's campaign.
Reporting live from Stoke, GB News' Political Editor Darren McCaffrey said: "Rishi Sunak needed a game-changer tonight, I'm not entirely sure he had it."
And appearing on Dan Wootton Tonight, former Chief Brexit Negotiator Lord Frost said he felt Ms Truss was the clear winner.
