The debate opened with a statement from both candidates which saw Mr Johnson promise to give the UK its "mojo" back, while Mr Hunt claimed he could have an appeal beyond the Tory party.
Throughout the debate, Mr Hunt referred to his past as a businessman, while Mr Johnson insisted he would negotiate a better Brexit deal with the EU due to his inflexibility over the deadline.
Although Brexit dominated the debate, the two candidates were pressed on their track records and perceived failures in Cabinet - with Mr Johnson quizzed about his work in trying to free jailed British-Iranian Nazanin Zaghari-Ratcliffe and Mr Hunt on doctors' contracts.
To start with the behemoth kicked off proceedings.
While both candidates believe they can negotiate a new deal with the European Union - despite the EU saying they will not reopen talks - there is one big difference between the two men: the deadline.
Mr Johnson has made a “do or die” commitment to leave the EU by the Halloween deadline.
Meanwhile Mr Hunt has said that while this is his preferred option, and he would countenance a no-deal Brexit "with a heavy heart" if a new deal with the EU looked likely but required the deadline to be pushed back, this would be something he would do.
As they debated the deadline, Mr Hunt said he is "just as keen" as Mr Johnson to take the UK out of the EU by the deadline of October 31, and far more likely to do so.
The Foreign Secretary told his predecessor "you shouldn't make promises you can't keep" as the pair clashed over the deadline, and said it would be a "breach of trust" to pledge to leave the EU by Halloween, and then fail to do so.
Instead, the Uxbridge MP said it was "vital" that the UK did leave by the deadline, otherwise the Government and Conservative Party would "haemorrhage trust".
He added it was "totally defeatist not to set a hard deadline".
By insisting that the UK will leave at the end of October, the ex-mayor of London said this would mean the UK would have a strong negotiating position with the EU and secure a better deal.
Mr Johnson, in a swipe at his rival, said the EU will not take the UK seriously if there is a "papier-mache" Brexit deadline - referring to Mr Hunt saying that he would be prepared to delay the Brexit deadline if it meant securing a deal at a later point.
"Nor will business understand that they must prepare for no-deal," he added.
The Foreign Secretary, whose birthday is on November 1, earlier said "nothing would be a better birthday present than knowing we have left on the 31st October".
Mr Hunt also warned that being so inflexible about the Brexit deadline could result in a general election before Brexit was delivered.
The Foreign Secretary also accused Mr Johnson of simply "peddling optimism" over Brexit.
"Being prime minister is about telling people what they need to hear, not just what they want to hear...
"We need leadership that is going to guide us through a big constitutional crisis and make a great success of Brexit, that means being honest with people about the challenges."
Would Mr Johnson resign if he failed to achieve Brexit by October 31?
When pressed by Mr Hunt and moderator Julie Etchingham, Mr Johnson refused to be drawn on whether he would resign or not if he became prime minister and the UK did not leave the EU by the deadline he has insisted on.
Mr Johnson said he would not commit to this because he did not "want to hold out to the EU the prospect that they encourage my resignation by refusing to agree a deal".
Adding that the only person who was not committing to anything was Mr Hunt who was "clearly not committed to coming out of the EU on October 31".
Cost of no-deal Brexit
While fears have been mooted over the cost of no-deal to the UK's economy, Mr Johnson said if the country prepared correctly, this cost would be "vanishingly inexpensive".
Would the candidates be prepared to suspend Parliament in order to force through no-deal?
If no-deal looks likely, MPs could vote against it and block it.
Previously in the Tory leadership race, candidates have mooted the idea of suspending Parliament to stop such a vote taking place, ensuring a no-deal Brexit would happen.
When questioned if they would be prepared to do this, Mr Hunt suggested he would not.
"When that has happened in the past, when Parliament has been shut down against its will, we actually had a civil war.
"I think it would be a rather curious thing to do, if this is about taking back control for Parliament, to actually shut it down."
Mr Hunt challenged Mr Johnson to rule it out, but the former London mayor said: "I'm not going to take anything off the table, any more than I'm going to take no deal off the table.
"I think it's absolutely bizarre at this stage in the negotiations for the UK - yet again - to be weakening its own position."
The backstop and the Irish border
Both men acknowledged that the backstop would need to be renegotiated in order to secure a better deal.
Mr Johnson said he would ensure frictionless movement by carrying out goods checks away from the border using technology that already exists, although when pressed by Etchingham that the EU had said such technology does not exist, the 55-year-old insisted that it did.
He added he would deal with the issue of the Irish border during the implementation period.
However, you only have an implementation period if a withdrawal agreement has been passed, and the EU has previously said it will not pass a withdrawal agreement until the issue of the Irish border is settled.
Meanwhile Mr Hunt said he would ensure mobile checks for food products, employ a trusted trader scheme, and use technology that already exists.
US diplomatic spat
Away from Brexit, the pair were quizzed about the surrounding the UK's ambassador to the US after emails from him were leaked in which he called the Trump administration "inept", "incompetent" and "uniquely dysfunctional".
In turn, Mr Trump responded by calling the ambassador, Sir Kim Darroch, "a very stupid guy" and saying he would no longer work with him, essentially pressing the Government to sack the 65-year-old, and also attacking "foolish" Theresa May over Brexit.
The Foreign Secretary stood by his previous comments that the Government backs Sir Kim, and expects its ambassadors to offer frank assessments of the countries they are in.
He added that if he became prime minister he could "certainly keep him (Sir Kim) until he is due to retire" at the end of 2019.
Suggesting that Mr Trump had no right to be telling the UK who should be its ambassador, Mr Hunt said it was a "matter for the United Kingdom".
Unlike Mr Hunt, Mr Johnson refused to say whether he would keep Sir Kim in post if he were to be prime minister, adding that whoever had leaked the documents "deserves to be eviscerated".
Boris Johnson is challenged on his comments about Nazanin Zaghari-Ratcliffe
The two men were also challenged about their perceived failures while in Cabinet.
Mr Johnson was questioned on his comments about Nazanin Zaghari-Ratcliffe during his time as foreign secretary.
The Tory leadership hopeful had wrongly stated that the British-Iranian prisoner was training journalists, something that was seized on by the Iranian regime who accuse the mother of being a spy.
Mr Johnson said he had "the utmost sympathy for her, for her family and the other cases that are similar", but refused to take any blame for what had happened.
He added: "It's very, very important that when you consider those cases that we all point the blame where it belongs, which is with the Iranian Revolutionary Guard who are detaining not just Nazanin but several others in a way that is inhumane, illegal and unfair.
"They are responsible and we should not inadvertently exculpate them in any way."
Jeremy Hunt is challenged about the junior doctors' strike
Meanwhile former health secretary Mr Hunt was challenged about the junior doctors' strike over an unpopular new contract.
He said he had been acting to tackle a problem of excess deaths at weekends.
What do the two men admire most in each other?
Asked what quality they most admired in their opponent as a future prime minister, both men struggled to give a straight answer.
Mr Johnson said: "I greatly admire his (Mr Hunt's) ability to change his mind and campaign for Brexit now and I think that's a very important attribute."
While Mr Hunt said: "I really admire Boris's ability to answer the question.
"I think he has this great ability - you ask him a question, he puts a smile on your face, and you forget what the question was.
"It's a brilliant quality for a politician, maybe not a prime minister though."
The two rivals for the Tory leadership clashed over tax policy, with Mr Hunt defending his measures to cut costs for businesses and attacking Mr Johnson for pledging to cut taxes for the wealthy.
Mr Hunt acknowledged his own plans were "not the most popular tax cuts" but "I want to boost the growth rate of our economy".
He said Donald Trump had cut business taxes and America was now growing at twice the rate of the UK.
"If we grew at 3%, 3.5% we would have an extra £20 billion to spend on tax cuts for people on low incomes... or our precious public services," Mr Hunt said.
He added that his "priority for tax cuts would be people on low incomes".
Mr Johnson said: "My agenda would be to focus on those who are hardest pressed."
He said he would increase National Insurance thresholds for those on low incomes but also defended his plans to cut taxes for people earning more than £50,000 as "part of a package".
He said public servants were being "dragged into the higher rates of taxation and that seems to me to be a legitimate subject for Conservatives to focus on and to want to fix as well".
Mr Hunt retorted: "I have spent my life trying to persuade people that we are not the party of the rich.
"If your very first tax cuts are for higher rate earners that's the wrong message."
Mr Johnson responded: "My programme is for a wide-ranging package, starting with people on low, modest incomes."
The debate comes after the 160,000 Tory party members received their ballot papers to vote for their next leader over the weekend.
The ballot closes on Monday, July 22, and the new leader, and the country's next prime minister, will be announced a day later.
The new prime minister will take over from Theresa May on Wednesday, July 24.
Watch the full debate here: