Sunak and health minister Sajid Javid sent resignation letters to Johnson within minutes of each other. Both took aim at his ability to run an administration that adhered to standards.
Signalling his intention to stay in power for as long as possible, Johnson quickly appointed former businessman and current education minister Nadhim Zahawi as his new finance minister.
Steve Barclay, appointed to impose discipline in Johnson's administration in February, was moved to the health portfolio.
The resignations came as Johnson was apologising for appointing an MP to a role involved in offering pastoral care, even after being briefed that the politician in question had been the subject of complaints about sexual misconduct.
Sunak and Javid are the first two ministers in the cabinet to resign, with other senior figures expressing support for Johnson.
Foreign minister Liz Truss, considered a leading contender to replace him, said she was "100 per cent behind the PM".
Four other MPs quit junior government roles while a trade envoy stood down and a vice chairman of the Conservative Party resigned his post on live television.
The resignations come after months of scandals and missteps, with Johnson so far weathering criticism over a damning report into parties at his Downing Street residence and office that broke COVID-19 lockdown rules and saw him fined by police.
There have been other policy U-turns, an ill-advised defence of another politician who broke lobbying rules, and he has also come under fire for not doing enough to tackle a cost-of-living crisis, with many Britons struggling to cope with rising fuel and food prices.
Economists say the country is heading for a sharp slowdown or possibly a recession.
Sunak and Javid had previously publicly supported Johnson, but in their letters said enough was enough.
Sunak, who had reportedly clashed with the prime minister in private about spending, said: "For me to step down as Chancellor (of the Exchequer) while the world is suffering the economic consequences of the pandemic, the war in Ukraine and other serious challenges is a decision that I have not taken lightly.
"The public rightly expect government to be conducted properly, competently and seriously.
"I recognise this may be my last ministerial job, but I believe these standards are worth fighting for."
Javid said many MPs and the public had lost confidence in Johnson's ability to govern in the national interest.
"It is clear to me that this situation will not change under your leadership - and you have therefore lost my confidence too," his letter said.
The resignations came minutes after Johnson went on television to apologise for appointing MP Christopher Pincher to a role involved in offering pastoral care in the Conservative Party, his latest public expression of contrition for his mistakes.
"I just want to make absolutely clear that there's no place in this government for anybody who is predatory or who abuses their position of power," Johnson said.
Pincher's resignation last Thursday triggered days of a changing narrative from Downing Street over what the prime minister knew of the deputy chief whip's behaviour and when he knew it.
Earlier on Tuesday after a former top official accused Johnson's office of lying, the prime minister's spokesman was forced into a quick about-turn to say the British leader had been briefed in "some form" about the case but had forgotten about that last week.
Some Conservative politicians are trying to renew attempts to unseat him, a month after the prime minister survived a confidence vote, while others earlier appealed to his cabinet ministers to move against Johnson.
"He's finished," said one previously loyal Conservative lawmaker on condition of anonymity.
"He shouldn't prolong the agony. It's disrespectful to his colleagues, his party and his country."
Opposition Labour leader Keir Starmer said those who had backed Johnson were complicit in how he had performed his job.
"After all the sleaze, the scandals and the failure, it's clear that this government is now collapsing," he said.
