Months of parliamentary deadlock, which risked the government running out of money to pay public servants and run programs, culminated in Mr Whitlam's dismissal as prime minister on 11 November, 1975.
Mr Whitlam was summoned to the residence of governor-general Sir John Kerr, who told him he'd been sacked as prime minister and opposition leader Malcolm Fraser would be installed in the job instead.
Mr Keating said the saga was "destructive" and revealed he urged the prime minister to go directly to Queen Elizabeth II to have Sir John sacked.
"In the event that Kerr resisted, I said to Gough he should be put under police arrest," the former Labor leader told journalist Niki Savva in an interview played at Old Parliament House to mark 50 years since the momentous day.
"That is certainly what I would have done if I was prime minister."
Mr Keating, who was the minister for northern Australia in 1975, was with Mr Whitlam and Sir John in the days before the fateful event.
He said he saw the pair laughing together in a meeting, which added to the deceit surrounding the sacking just four days later.
After the meeting, Mr Keating recalled Mr Whitlam getting into a Mercedes before saying, "Well, he seems alright ... he's entirely proper, he'll do the right thing."
That was how the governor-general lulled Mr Whitlam into a false sense of security, the former prime minister said.
"It was the brutality and malevolence of it all, really, which was so striking but not immediately apparent on the day," Mr Keating said.
Mr Keating's successor, former Liberal prime minister John Howard, said Sir John had been unfairly criticised in the 50 years after the dismissal.
"Fate cast him in a very difficult position," he told journalist Barrie Cassidy in a separate interview at Old Parliament.
"(Fraser) and Whitlam together were two very determined men who were ruthlessly intent on their objectives," Mr Howard said.
Australia's second-longest serving prime minister also suggested a number of changes to parliamentary processes to smooth the operations of government, including fixed four-year terms.
"I would say to (Opposition Leader) Sussan Ley, to the prime minister, get together on it now and don't attach conditions," he said.
Governor-General Sam Mostyn said it was unlikely such a series of events would ever play out again, although she added she would continue her role "consistent with the conventions of this office".
"I could not imagine a situation in modern Australia where a prime minister would be surprised or blindsided by the governor-general in the same circumstances that occurred in 1975," she said.
Ms Mostyn added there was a "strong mosaic" of checks and balances which helped underpin Australia's system of government.
Prime Minister Anthony Albanese defended the Whitlam legacy while announcing a statue of the former Labor leader would be erected outside Old Parliament.
"The dismissal was a calculated plot, hatched by conservative forces which sacrificed conventions and institutions in the pursuit of power," he said.
