Voters in the Melbourne seat will head back to the polls on Saturday, less than a year after the last federal election, following the resignation of Liberal MP Alan Tudge.
Mr Dutton told coalition MPs at a joint party room meeting the by-election would be a tight contest, and stressed the need for a united front.
It follows the decision by the Victorian Liberals to suspend state MP Moira Deeming for nine months for speaking at an anti-trans rights rally that was crashed by neo-Nazis.
"We can see in Victoria at the moment the damage that can be caused and the opportunities lost when we don't act as a team and when we talk about ourselves," Mr Dutton told the meeting.
"We should never feel complacent about this. That is going to be a tight race. It's going to be hard fought."
The Liberals hold Aston by 2.8 per cent, after the party suffered a more than seven per cent swing against it at the last election.
But a sitting government has not won a seat off the opposition at a by-election for more than 100 years.
Former union organiser Mary Doyle is the Labor candidate, while the Liberals are running Melbourne City councillor Roshena Campbell.
Senior lecturer in politics at Monash University Zareh Ghazarian said while history may be against the government, the Liberals could be on unsteady ground.
"It would seem to be an automatic Liberal win, but with the factors we are seeing here - unpopular Victorian Liberals, a longstanding MP retiring, people aren't turning up at the same rate - I suspect there are dangerous signs for the Liberal Party who may struggle to hold on to Aston," Dr Ghazarian told AAP.
"The momentum seems to be against the Liberals at the moment."
Victorian Labor senator Jess Walsh told parliament the opposition leader would be an asset.
"There is no better campaigner for Labor in the seat of Aston than Mr Dutton," she said.
The Australian Electoral Commission is concerned about a low voter turnout.
Electoral Commissioner Tom Rogers said pre-poll figures were down five per cent compared with last year's poll.
"By-elections have traditionally had less people participate than in a full federal election but it's just as important to have your say," Mr Rogers said.
"Typically, if someone casts their vote early in one election they'll do so in the next one as well, and we're not quite seeing that here which makes us worry about low participation."
The commission has sent out more communication to voters for the upcoming by-election than they have for any previous by-election.
More than 14,000 people had cast their votes at early voting centres as of Monday evening, down from the more than 18,540 voters at the same point last year.
There have been more than 17,500 applications for postal votes.
Dr Ghazarian said the low turnout may be due to election fatigue among voters.
"They've gone through the general election in May and the state election in November in Victoria and are maybe thinking three times in a year going to an election may be a bit much," he said.
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