Mr Dutton is campaigning in the seat in Melbourne's east with Ms Campbell on Friday as Labor also gets ready to make its final push for Aston ahead of Saturday's by-election.
The by-election is shaping up as the first electoral test of Mr Dutton's leadership since the federal coalition lost government in May last year.
The Liberals hold the seat on a slim 2.8 per cent margin after a massive swing against the party at the 2022 election when it was held by Morrison government minister Alan Tudge, whose resignation triggered the upcoming poll.
Mr Dutton is trying to win over Aston voters by focussing on rising energy prices and other cost of living pressures.
He says while the result will be tight, the Liberals should hold onto the seat.
"Every decision Labor has taken economically over the course of the last 10 months has driven up the cost of living pressures on families and on small businesses," he said on Friday.
"There's an opportunity here to send a message to Labor, that it's just not good enough because living pressures continue to go up."
He's also trying to tap into local anger about the Victorian Labor government's road funding priorities.
"They cut road funding, and at a time when people are experiencing more and more frustration on the way to work," Mr Dutton said.
"It's about sending a person to Canberra who will be a strong local representative and Roshena Campbell is exactly that person."
Ms Campbell is hoping her experience as a barrister and Melbourne City councillor will position her to win the seat.
"Labor not having a plan is causing real anxiety in this seat," she said.
"They have shown they are happy to take the outer east for granted."
Prime Minister Anthony Albanese said his government had done "an enormous amount" in 10 months, including passing legislation this week to cap pollution from big emitters and start a $15 billion manufacturing fund.
"We need stability and (Labor candidate) Mary Doyle will be a voice in government for the people of Aston," he told ABC radio.
"Mary Doyle will actually be able to get things done for her local community."
But Mr Albanese admitted Labor would be hard-pressed to win the seat.
"In 2019, the then local member Alan Tudge got 54.7 per cent of the primary vote," he said.
"So it would be astonishing if the Liberal Party didn't get a two-party preferred (vote) with a six in front, frankly."
Labor cabinet minister Jason Clare said Mr Dutton's unpopularity in Melbourne could dent the Liberal party's showing.
"Peter Dutton isn't the most popular fellow in Melbourne," he said.
"One thing is for sure though, the Liberals are the red hot favourites here. No government has won a by-election from opposition in 100 years.
"We couldn't win the seat of Aston at the last election last year and we had (former Liberal prime minister) Scott Morrison working for us."