Fanning fears of Muslim immigrants "stealing jobs" and "sympathizing with Islamic State [IS, formerly ISIS]", Anning offered: "The final solution to the immigration problem is, of course, a popular vote".
A member of the minor Katter's Australian Party, Anning was unapologetic about using the same phrase Nazi leaders used in planning the Holocaust during World War II.
"Senator Anning has spat in the face of our successful multicultural society, but I wouldn't expect anything less from an ex-One Nation senator", she said.
"We do not want people coming in from the Middle East or North Africa unless they're the persecuted minorities. Australia is a warm and open nation".
"Because you may have your grievances with what Fraser Anning has said, don't direct them at me - it's got nothing to do with me".
Such are the rituals of first speeches that many Coalition senators and even crossbencher Derryn Hinch (who has been beating up on himself publicly ever since) went over to pay Anning the traditional congratulations afterwards. He claimed that the majority of Muslims in Australia were a burden to society. "That is an unacceptable use of the term", he told ABC Radio on Tuesday.
But after that reactions were quick, and by Wednesday morning condemnation was raining down on Anning from nearly everywhere.
A trailblazing Muslim MP says better awareness of the sustained racist abuse some endure could help parliaments look more like Australia's streets and suburbs.
"You have to be pretty outrageous to be condemned by everybody in the Australian parliament, but Senator Anning has managed to do just this", he said.
Around 1942, the Nazi leadership established a plan called "The Final Solution to the Jewish Question", which led to the genocide of more than six million Jewish people in occupied Europe.
The senator also drew criticism for suggesting that Australians could return to the "White Australia" policy, which placed heavy restrictions on non-European immigration until the late 1960s.
The Greens called on Mr Katter to expel the Queenslander from his party, with leader Richard Di Natale calling Senator Anning "a myopic red-neck reaching out from another time to another people".
"So we reject, we condemn racism in any form, and the remarks by Senator Anning are justly condemned and rejected by us all", he said.
Anning, who has been in parliament for less than a year has entered into a lose alliance with several conservative independent lawmakers that has boosted his otherwise inconsequential role in Australia's upper house.
Mr Anning also called for a complete ban on Muslim immigration and linked Muslim communities to terrorism and being on welfare programmes.
"Now, as I said, I'm appalled by Fraser Anning's speech".