Detective Chief Superintendent Joanne Shanahan, 55, and Tania McNeill, 53, died in the Urrbae crash on Saturday afternoon.
Det Chief Supt Shanahan had been a passenger in a car driven by her husband Peter, a retired police detective who is currently the general counsel for SA Police.
He was taken to Royal Adelaide Hospital with with non-life-threatening injuries and later released.
Ms McNeill, a mother-of-one, had been driving alone.
A 20-year-old man driving the third vehicle remains in hospital with life-threatening injuries.
SA Police Commissioner Grant Stevens held back tears on Sunday as he told reporters Det Chief Supt Shanahan was a “dear friend”.
“Sadly, the real tragedy of road fatalities has been brought home to South Australia police yesterday when we lost one of our finest senior police officers,” he said.
The mother-of-two joined the force in 1981 and was appointed the inaugural officer in charge of the family and domestic violence branch.
She was awarded an Australian police medal last year and was a highly respected leader, Stevens said.
Most recently, she had a leadership role in the police operation centre for SA’s response to COVID-19.
“Not only have we lost a beautiful person, but we’ve lost an officer with a wealth of knowledge,” Stevens said.
Police Association President Mark Carroll described Det Chief Supt Shanahan’s death as a crushing loss.
“A woman of solid intellect and great application, she had worked in a range of investigational and other fields,” he said.
“For many of those who worked with Joanne and/or knew her on a personal level, the pain of losing her, so suddenly and unexpectedly, is certain to be overwhelming.”
Carroll also acknowledged Det Chief Supt Shanahan had been devoted to her family.
“The true measure of the value of her presence in their lives will be evident in the decades to come,” he said.
“It will lie in all the precious family moments of which an unjust death has robbed a close, loving family.”
McNeill’s family released a statement, saying words could not describe their pain.
“Tania was a loving, vibrant lady who enjoyed a good laugh,” they said.
“She was a kind and loving mother, wife, daughter and sister, who would do anything for anyone.
“Tania’s loss will be deeply felt by so many forever.”
Major crash officers are investigating and appealing for witnesses to contact police.
The crash follows the deaths of four police officers who were struck by a truck while dealing with Porsche driver Richard Pusey in the emergency lane of a freeway in Victoria last Wednesday.