Akon Guode, 37, killed one-year-old Bol and four-year-old twins Hanger and Madit in Melbourne's south-west in 2015.
Another child, six-year-old Alual, was also in the car but survived.
In the Supreme Court of Victoria, Guode pleaded guilty to one count of infanticide, two counts of murder and one of attempted murder.
She entered her pleas with help from an interpreter. Guode arrived in Australia from South Sudan in 2008.
Joseph Manyang, the father of the three children, told a hearing last year that Guode said she felt dizzy before the crash.
He described Guode as a "loving mother" who would not have harmed the children intentionally.
However, a key witness told police in a statement that Guode spoke about killing her children on the day of the tragedy.
Passersby and emergency crews tried desperately to rescue the children in the moments after the car entered Lake Gladman in Wyndham Vale.
A harrowing emergency call from one witness was played during a court hearing last year.
"I saw them deliberately drive in there, well it looked like that anyway," Alexandra Colson-Ing said, according to The Age.
After moving closer to the scene, she said: "They are floating, they are floating in the water. (They) can't swim."
Guode and her daughter Alual were rescued.
Guode has been remanded in custody until her next court appearance on 31 January.
A mother has admitted killing three of her children by driving them into a lake in southern Australia.