The Nissan car Mahu was driving swerved across the median strip and police had to brake to avoid hitting her, the court heard.
When police pulled her over they found Mahu's 3-year-old son sitting unrestrained on her lap and clutching the steering wheel.
Mahu blew 867mcg of alcohol per litre of breath, more than three times the 250mcg limit.
She told police she had drunk two boxes of Vodka cruisers the previous night. She said her son had "gone crazy" in the back seat of the car so she allowed him into the front.
Judge Simon Menzies convicted Mahu and remanded her on bail until sentencing on November 17.
He reminded Mahu a condition of her bail was that she not drive.
In the dock Mahu stood with her back to public gallery.
She left the court quickly and a friend yelled at a Herald reporter as they drove off.
