Leaving the water running, the woman began doing other household chores including washing, mopping and dishes.
The older brother called out from the bath several times but the mum did not register it was a cause for alarm.
It took between 16 and 24 minutes for the bath tub to fill.
When the woman returned the younger boy was lying face down and unresponsive.
She grabbed him out and attempted to do CPR.
The 11-month-old was admitted to intensive care at Starship children's hospital where investigations showed that he had sustained non-survivable brain damage.
Justice Cooke said unfortunately tragic cases like this happened from time to time.
The judge considered three similar cases in which the accidental death of a child had occurred during a period of inattention.
In the first case a seven-month-old drowned in "very similar circumstances".
The child was left in a bath tub with the shower running when his mother took a roughly 20 minute phone call.
"During that period the plug hole became blocked by a toy and he drowned."
In that case the woman was convicted and discharged, much as the Crown seeks here, he said.
In the second case, a 22-month-old drowned in the family swimming pool when her
mother left her with other older children to attend to her two-week-old baby.
After assessing the impact on the defendant and the defendant's family, she was discharged without conviction.
In the third case, a mum who usually dropped her 16-month-old at day care while on her way to work was distracted.
Functioning on autopilot she forgot to turn off to go to day care.
It was several hours later that her son was found in the car outside her work. He had died of heatstroke and dehydration.
"It seems to me that the present case also involved a similar blanking of mind in circumstances when you were exhausted," Justice Cooke said.
"You had noted that the plug was in the hole, and that you needed to take it out. But you simply failed to do so as you usually do."
As in those three other cases, she had made a mistake, Justice Cooke said.
"Parents make mistakes all the time," he said.
"The fact that it had such tragic consequences here does not mean it wasn't just a mistake."
For a parent the pain and ongoing distress arising from the loss of the child was punishment enough, he said.
The judge deemed a conviction was not necessary when the woman had appeared in court acknowledging before her community that she made a mistake that resulted in the death of her child.