Former chancellor Rishi Sunak once again topped the ballot among Tory MPs in the fourth round of voting, with 118 backing him – just shy of the number effectively guaranteeing him entry to the final phase.
But Ms Truss, the foreign secretary, picked up 15 votes to command the support of 86 Tory MPs, as the right of the party appears to be coalescing around her.
Penny Mordaunt increased her share by ten to sit on 92, while Ms Badenoch came last on 59 votes, meaning she has now been eliminated from the contest.
Ms Truss is believed to be more likely than Ms Mordaunt to pick up a significant number of those 59 votes during the final vote by MPs on Wednesday.
This momentum means the foreign secretary is now seen as the favourite to face Mr Sunak in the final two.
And while the former chancellor enjoys the support of more Tory MPs, it is party members who will ultimately decide the winner by postal ballot.
Polling by YouGov suggested Mr Sunak would lose against both of his remaining challengers in a vote by Tory members.
The survey of 725 party members had Ms Truss beating Mr Sunak by 54 per cent to 35 per cent and Ms Mordaunt beating him by 51 per cent to 37 per cent.
The current size of the Conservative membership is unknown, but at the last leadership election in 2019 there were around 160,000 members, meaning the polling is limited.
Earlier, Mr Sunak pledged to do “anything and everything” to strengthen the Union as he insisted only he can beat Labour at the next general election.
He raised the prospect of a deal between Labour and the SNP and pledged to “confront this threat early”.
Labour leader Sir Keir Starmer has repeatedly ruled out any deal or coalition with the SNP.
Mr Sunak said: “This leadership contest is about more than just being the leader of our party, it’s about becoming the custodian of our United Kingdom.
“We can’t rule out a deal between the Labour Party and the Scottish Nationalists at the next general election, so it’s important that we confront this threat early.
“This means a UK Government who is willing to roll up their sleeves and get stuck into creating jobs, growth and prosperity in all corners of the UK, from Llandudno to Perth, Belfast to Birmingham.
“There is nothing more Conservative than our precious Union, and everything great that we have achieved we have done so as one family.
"For all of these reasons, my Government will do anything and everything to protect, sustain and strengthen it.”
Mr Sunak said he would abandon Westminster’s “devolve and forget” mentality and instead oversee the most active UK-wide Government in decades.
He also ruled out agreeing to another independence referendum.
Ms Mordaunt, the trade minister, said: “We are so nearly across the finish line. I am raring to go and excited to put my case to members across the country and win.”
She thanked Ms Badenoch, the former equalities minister, and praised her “fresh thinking and bold policies” in a possible pitch to begin winning over her now-floating voters.
Ms Truss earlier promised to increase defence spending by 2030 and strengthen the intelligence services.
Her campaign urged Ms Badenoch’s supporters to unite behind the foreign secretary.
A spokeswoman said: “Kemi Badenoch has run a fantastic campaign and contributed enormously to the battle of ideas throughout this contest.
“Now is the time for the party to unite behind a candidate who will govern in a Conservative way and who has shown she can deliver time and again.
“Liz has a bold new economic agenda that will immediately tackle the cost-of-living crisis, boost economic growth and continue leading the global fight for freedom in Ukraine.”
Ms Badenoch said she was “grateful” to the Tory MPs and party members who had backed her campaign.
She said: “This campaign began less than two weeks ago. What we’ve achieved demonstrates the level of support for our vision of change for our country and for the Conservative Party.”
Anne-Marie Trevelyan, the international trade secretary, came out in support of Ms Truss on Tuesday after previously backing eliminated candidate Tom Tugendhat.
She said the foreign secretary “will bring strong Tory economy policy, understanding of our responsibilities on the world stage and strength to deal with the tough choices”.
Transport secretary Grant Shapps, who is backing Mr Sunak, insisted on LBC radio the former chancellor is a “huge fan of levelling up”.
The candidates took part in more behind-closed-doors hustings with the Northern Research Group of Conservative MPs and Onward think-tank on Tuesday evening.
SNP Westminster leader Ian Blackford said: "While the Tory leadership race continues to contest in a rabid race to the right, one thing remains clear: whoever wins, Scotland will lose.
"The Westminster system is fundamentally broken. Whether it's Rishi Sunak, Liz Truss or Penny Mordaunt – Scotland will find itself stuck with a government it did not vote for, nor has voted for since 1955.
"The Scottish Government was given a cast-iron democratic mandate by the people of Scotland to hold an independence referendum, and that is exactly what we intend to do.
"No Trump-like efforts from any Tory politician can deny that democratic reality."
Mr Johnson had earlier used his final Cabinet meeting to defend his record in office as Tory leadership contenders sought to break from the policies he championed.
The Prime Minister said his decision to commit to net zero carbon emissions by 2050 to tackle climate change was right, even though it had become “unfashionable”. The target has been criticised by some of his potential successors because of the economic risk.
The leadership rivals have also clashed over how to address the cost-of-living crisis, but Mr Johnson said the “fundamental strength” of the economy had already allowed his administration to offer help to the most vulnerable.
All three remaining candidates have expressed concern about the net zero goal.
Ms Truss, who was sat opposite the Prime Minister at the Cabinet meeting, has said the goal should be delivered in a way that “doesn’t harm people and businesses” and has promised to shift green levies from energy bills.
Mr Sunak has warned that if progress on the agenda is “too hard and too fast” it would lose public support.
Speaking as Westminster baked in a heatwave, Mr Johnson said: “With temperatures setting records in this country, who can doubt that we were right to be the first major economy to go for net zero?
“And I know it may be sometimes unfashionable to say this now, but it is the right thing to do.
“If we’re going to protect our planet and if we’re going to do the right thing to tackle global warming, it’s essential that we set that lead.”
He added it also offers a “massive economic opportunity to transition to millions of millions of clean, green technology driven jobs”.
Parliament rises for the summer recess on Thursday, returning on September 5 when the next Tory leader is expected to be announced.
Mr Johnson said the Cabinet meeting was taking place a year on from England’s “freedom day” when coronavirus restrictions were largely lifted.
He indicated the lessons from the pandemic would be applied in the current heatwave.
“On another scorching, sweltering day I think it’s very, very important that we think back to that moment that we opened up [after the lockdown] and try and balance risk with the need to keep our country, our society and our economy moving,” he said.