Both leadership candidates came out fighting against the Scottish National Party (SNP) during a grilling by Tory members in Perth.
The event was picketed by a few hundred supporters of Scottish independence who shouted “Tory scum” at attendees and threw eggs as people arrived at the hustings.
But Mr Sunak and Ms Truss did not hold back from laying into the SNP’s record, hitting out at Ms Sturgeon’s “barmy” calls for an independence vote.
And both candidates rejected Labour proposals to freeze the energy price cap at its current rate to keep soaring bills low.
Ms Sunak said he would “not be shy on calling out the SNP’s record on things like drug and alcohol abuse because it’s not good enough and Scottish people deserve better,” and said he wanted to end the “devolve and forget mentality”.
Referring to Ms Truss’s previous remarks that she would “ignore” Ms Sturgeon, he said: “I don’t want to just ignore Nicola Sturgeon, I want to take her on and beat her”.
Asked whether he would allow another vote on Scottish independence, he said: “I can’t imagine the circumstances in which I would… I don’t think that anybody thinks now or any time in the near future is remotely the right time to focus on this.”
He suggested Ms Sturgeon “doesn’t really” believe in devolution. “Devolution to her just means power to her,” he said. “I will not be shy of holding the SNP to account”.
The former Chancellor said politicians “should be relentlessly focused on addressing” cost of living concerns but dismissed Labour’s suggestion of freezing the energy price cap.
Asked if he would rule it out, he said: “Yes I don’t think that is the right approach.”
He reiterated he would want to wait until the figures for October’s energy prices were confirmed before announcing what further support payments families would receive, but he said: “I think the right way to do that is through direct support.”
Ms Truss ruled out another Scottish vote entirely and drew cheers from the audience when she said: “I will not allow another independence referendum.”
“We are family and I will never ever let our family be split up,” she told members.
She said she would “knock spots” off Ms Sturgeon as prime minister and “ignore these constant calls” for a vote that was “once in a generation”.
The Foreign Secretary accused the Scottish Government of “pursuing an agenda of separatism rather than dealing with issues they created in the Scottish education system, in the NHS and in the transport system”.
“I know the people of Scotland deserve better, and they want better,” she added.
Asked whether she would consider a price cap freeze to keep bills low, she repeated her criticism that it was a temporary “sticking plaster” and said her focus would be on tax cuts to help household and long-term plans to shore up energy supplies.
“What we need to do is deal with the supply issue,” she said, adding it was wrong to say “the answer is to tax more and spend more government money”.