The first in a string of TV leadership debates was dominated by issues of trust, with all five of the candidates failing to explicitly back Mr Johnson when asked if the Prime Minister was honest.
However, only senior backbencher Tom Tugendhat answered “no”.
Mr Sunak defended his record as chancellor as he attacked Ms Truss and Ms Mordaunt over their plans for tax cuts. The three are seen as frontrunners in the race for the Tory leadership.
Meanwhile, Ms Mordaunt clashed with Ms Truss and Ms Badenoch as they challenged her record on trans issues.
It came as Mr Sunak’s most prominent Scottish supporter, the MP Andrew Bowie, sparked a row after insisting the former chancellor would continue to bypass Holyrood in devolved areas through the UK Government’s “levelling up” agenda.
Writing in The Times, Mr Bowie said Mr Sunak "has led the pushback against the 'devolve and forget' mentality that permeates Whitehall”.
He added: "He knows that with their record in government, we cannot trust the Scottish National Party to act in the best interests of the Scottish people — only in the interests of the SNP."
First Minister Nicola Sturgeon hit back on Twitter, writing: “Good of the Tories to help make the case for independence.”
During the first TV leadership debate, held by Channel 4, the five Tory leadership candidates were asked to give a yes/no answer on whether Mr Johnson was honest.
Ms Badenoch said “sometimes”, while Ms Mordaunt said: “There have been some really severe issues and I think he has paid a price for that.”
Mr Sunak, whose resignation helped spark the Prime Minister’s downfall, said: “I tried to give him the benefit of the doubt for as long as possible and ultimately I reached the conclusion that I couldn’t, and that’s why I resigned… There were a number of reasons that I resigned but trust and honesty was part of that.”
Ms Truss, who is backed by many allies of Mr Johnson, said “he has been very clear himself that he made mistakes in Government” but she had taken his explanation for inaccurate statements over partygate “at face value”.
Asked the same question, Mr Tugendhat said: “No.”
Stressing the need to grip inflation, Mr Sunak told the Channel 4 debate: “We cannot make it worse, inflation is the enemy that makes everyone poorer. It erodes your savings, it erodes your living standards, it means that those of you who have mortgages will see your interest rates go up higher and higher.
“I don’t think the responsible thing to do right now is launch into some unfunded spree of borrowing and more debt, that will just make inflation worse, it will make the problem longer.”
Ms Truss pinned the blame on the Bank of England, saying “we have inflation because of our monetary policy, that we haven’t been tough enough on the monetary supply, that’s the way that I would address that issue”.
Mr Sunak told her: “Borrowing your way out of inflation isn’t a plan, it’s a fairy tale.”
Ms Truss responded: “I think it is wrong to put taxes up.”
The Foreign Secretary had earlier vowed to axe the planned corporation tax hike from 19 to 25 per cent next year as she made a multibillion-pound pitch for the Tory leadership during an online hustings.
She also committed to reverse the national insurance hike and implement a temporary moratorium on the green energy levy.
Ms Mordaunt told the debate her economic platform “is not based on tax and spend, it’s based on growth and competition.”
She has promised to cut VAT on fuel and increase income tax thresholds in line with inflation – something Mr Sunak said would cost around £15 billion.
He said: “Even the pledges you’ve made are double-digit billion pound promises. The best way to help everyone, the best way to make sure that they have money in their pocket, is to get a grip of inflation, and that should be everybody’s priority because that’s the thing that’s going to erode everyone’s living standards.”
Ms Mordaunt replied: “Two things, Rishi, that you haven’t realised – that is, I know you know people are going to need more help this autumn, but actually people need help now and you are going to have to do something on taxation.
“Next April we are going to be one of the most uncompetitive nations in terms of our tax competitiveness … that cannot be allowed to happen.”
Ms Truss joined in the attack on Mr Sunak, saying: “You cannot tax your way to growth.”
Meanwhile, Mr Tugendhat accused Mr Sunak of only agreeing to the National Insurance rise because the Prime Minister wanted it.
After the former chancellor challenged Mr Tugendhat on why he voted against the National Insurance rise last year, the backbencher said: "We had a long conversation about it, and you set out your position and I asked: why on earth this was going to be necessary? You told me because the boss wanted it."
All five candidates sought to emphasise trust and integrity.
Asked when she had stood up for integrity and honesty, Ms Truss said: “I stood by Boris Johnson, of course, I raised issues with him in private, but I supported him for the leadership election. I was part of his Cabinet and I owed him my loyalty.
“What I’m saying to you is that every statement I’ve ever made in government, I’m always somebody who has acted with honesty and integrity.”
Mr Tugendhat acknowledged that “trust in politics has been collapsing, trust in our party has been collapsing”.
He promised a “clean start” – the phrase which is his campaign slogan.
Ms Badenoch has said the outgoing Government rewarded loyalty to Mr Johnson, rather than talent.
Elsewhere, Ms Mordaunt was asked about the attacks on her campaign from rival wings of the Tory Party, including allies of Ms Truss. She said she took these as a “big fat compliment”.
Asked whether she “had the dogs out” to attack Ms Mordaunt, Ms Truss said: “I’m running an entirely positive campaign which is about the great challenges we face and what we need to do to deliver for the people of Britain because we are facing a cost-of-living crisis, families are struggling.”
She added: “I do trust all of the people who are on this platform with me.”
Ms Mordaunt, the former minister for women and equalities, also faced questions over her position on gender identity against claims that she previously supported gender self-identification – a controversial issue within the Tory Party.
She said she has “never been in favour of self-ID”.
Ms Badenoch said she found it difficult to accept this “because when I took over as equalities minister in 2020, the policy that was being pushed was self-ID”.
SNP Westminster Leader Ian Blackford MP said: “No matter who ends up Prime Minister at the end of this contest, Scotland loses.”