Brexit figurehead Mr Johnson goes as overwhelming favourite into the last phase of the long drawn-out contest to succeed Theresa May.
His tally of 160 in the fifth round of voting at Westminster amounted to more than half of the 313 Tory MPs.
Environment secretary Mr Gove - who had briefly moved into second place earlier in the day - was edged out by Mr Hunt by the narrowest of margins, taking 75 votes to the foreign secretary's 77.
The two survivors from last week's original line-up of 10 now go forward to a postal ballot of around 160,000 Conservative Party members in the country.
A series of more than a dozen regional hustings will start in Birmingham on Saturday, with Ms May's successor named in the week of July 22. ITV will host a TV showdown between the two contenders on 9 July, which both Johnson and Hunt immediately said they will attend.
Mr Hunt acknowledged he was the "underdog" in the national showdown, after polling suggesting the former London mayor is the favourite of Tory members.
But he insisted: "In politics surprises happen, as they did today."
Mr Johnson is widely considered to prefer a run-off against Mr Hunt, who backed Remain in the 2016 EU referendum and has been portrayed by rivals as the "continuity May" candidate.
His success in leapfrogging Mr Gove into second place has sparked renewed speculation at Westminster about the possible "lending" of supporters by the Johnson camp to get the foreign secretary over the line.
Mr Hunt picked up 18 supporters to Mr Gove's 14 after the elimination of Sajid Javid earlier in the day. The increase of three in Mr Johnson's vote tally was fewer than the four Javid supporters who had announced during the day that they were switching to him.
The Johnson camp have consistently rejected any suggestion of dirty tricks as "nonsense".
And Hunt backer Greg Hands denied any lending of votes, saying: "I have seen no evidence of that – it was a contest fairly and squarely fought."
Mr Gove's campaign manager Mel Stride agreed: "We didn't see a situation where - as some had speculated - a very large number of votes might have transferred from Boris Johnson to Jeremy Hunt.
"It would appear to me everybody has behaved pretty much as one would hope they would."
Mr Johnson said he was "deeply honoured" to have secured the support of more than 50 per cent of Tory MPs, adding: "I look forward to getting out across the UK and to set out my plan to deliver Brexit, unite our country, and create a brighter future for all of us."
But Labour's national campaign co-ordinator Andrew Gwynne said the country's prime minister should be decided by a general election, not "a handful of unrepresentative Conservative members".
"What a choice - the man who broke the NHS or the man who wants to sell it to Donald Trump," said Mr Gwynne.
Brexit hardliner Dominic Raab rejected suggestions that the former foreign secretary was softening his stance on EU withdrawal, having declined to guarantee departure by the 31 October deadline during a TV debate. Pressed on the BBC broadcast to give a hard and fast guarantee, Mr Johnson said only that it was "eminently feasible".
Mr Raab - who swung behind the former London mayor after being eliminated in the second round of voting - said Mr Johnson's comment had been "over-interpreted".
And he added: “I talked to him before I came out in support and he remained very clear on that commitment."
Robert Buckland, a Johnson backer who voted Remain in the referendum, said: “My view is that Boris’s policy is to avoid a deliberate crash-out, he wants a deal”.
Mr Hands described the foreign secretary as “the man who can open the door in Brussels”, saying the Hunt camp “hope” to leave on 31 October. But he added: “We are not going to die in the ditch....if it takes a bit longer, so be it”
Mr Gove - who also failed in a bid for prime minister in 2016 - said he was "naturally disappointed" not to make it to the final two, but "so proud of the campaign we ran".
"It’s been an honour to be able to set out a vision for the future of our great country." he said. "Many congratulations to Boris and Jeremy."
Mr Stride said the environment secretary's admission of youthful cocaine use had damaged his leadership bid: "It stalled us and meant momentum was lost at that time."
Mr Hunt said: "I'm the underdog - but in politics surprises happen as they did today. I do not doubt the responsibility on my shoulders - to show my party how we deliver Brexit and not an election, but also a turbo-charged economy and a country that walks tall in the world."
Ms May's effective deputy prime minister David Lidington, who previously backed Rory Stewart, implored candidates to "look beyond Brexit" as the campaign enters its final straight, warning that the Tory Party is "facing an existential crisis" and needs to find younger supporters.
"You have to think back to 1992 since the Conservative Party last won a clear overall majority," said Mr Lidington. "If you're going by age group, you have to get to 51-year-olds before you find more people willing to vote Conservative than Labour."
Work and pensions secretary Amber Rudd - who had originally been expected to back Mr Johnson but in fact campaigned for Mr Hunt - said the results were "absolutely fantastic" for the foreign secretary and that he was "the best man to unite the country".
Announcing the result in a Westminster committee room, the acting co-chair of the backbench 1922 Committee Dame Cheryl Gillan revealed that all Tory MPs had voted, with just one spoilt ballot.
Opponents of Brexit voiced concern that the new PM may not be in place in time to face scrutiny from MPs - and a possible confidence vote - before parliament rises for its five-week summer break on 25 July.
After the dates of the summer recess were announced, Labour MP Owen Smith, a leading supporter of the People's Vote campaign, said: “It is outrageous that this tattered government is planning to let Boris Johnson get five weeks without facing any sort of Parliamentary scrutiny.
“The clock is ticking down on the precious extension negotiated with the EU in March. Before long we will be back on a cliff-edge so this is no time to head for the beach."
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