Thugs put an oily rag through the letterbox and then set it alight shortly after she and comic Lenny moved in together.
“It was massively shocking to me,” said Dawn, 56.
“Someone put an oily rag through our front door and tried to burn us down.
“Luckily I woke up and smelt it, otherwise I’m not sure we would be here.”
Dawn, who adopted mixed-race daughter Billie, now 23, with Lenny, 55, is worried that racist attitudes have not changed in 30 years.
And she believes that her daughter and ex-husband – who recently found himself at the centre of a race row after a UKIP candidate said he should leave Britain to live in a black country – are experiencing “stealth racism”.
Dawn said: “It’s the little snidey comments or things people think it is OK to say, a kind of gradual erosion that I find particularly dangerous.”
The pair, who split in 2010 after 25 years of marriage, have previously spoken of other shocking abuse they suffered as a mixed-race couple.
They were once targeted by members of the Ku Klux Klan, who smeared excrement on their front door and doorstep and daubed graffiti on their walls.
Dawn spoke out on BBC Radio while promoting her first solo touring show about her life, Thirty Million Minutes.
She also opened up about her body image.
“You’re just never allowed to be anything other than a fat woman,” she said.
“And I thought, let me have control of this. If I can talk about things in my own voice and control how it is said, then that is best.”
Dawn refuses to talk about her new husband, charity boss Mark Bignell, 51, in her stage show.
But she revealed she has nicknamed him her “sacrificial anode”.
She said: “A sacrificial anode is a piece of metal which is put on the side of a boat, usually a big boat, and it gathers all the corrosion and the rust to it, so that the boat survives for longer. And that is how I regard him.”
Asked how they met she added: “He had known my mother for years and was a colleague of hers, helping people with drug and alcohol problems.
“I hadn’t noticed him as I was happily married. Then I did notice him and that was that.”
Ukip candidate William Henwood was forced to resign from the party last month after he suggested Lenny should emigrate to a “black country”.
His remark came after Lenny launched a campaign to have more people from ethnic minorities on British TV and media.