Wildcard Barty's 6-4, 5-7, 6-3 win sets up an all-Australian clash in the second round against 14th seed Samantha Stosur.
But for the 23-year-old Bouchard, a former world number five who has slumped to 56th in the world rankings, it was another blow after her first round exit in Indian Wells.
"It's been a bit of a struggle,” said a stone-faced Bouchard, who was unable to account for her loss of form.
Bouchard was a beaten finalist at Wimbledon in 2014 but, apart from a run to the semifinal at Sydney, where she was beaten by Britain's Johanna Konta, she has been unable to make an impact this year.
Barty reproduced the gutsy tennis that helped her secure her maiden WTA title at the Malaysian Open in Kuala Lumpur last month.
"We've had a good pre-season and get a good foundation and the stars aligned a bit for us this year so far. We have worked hard and it is just that hard work starting to pay off," said the Australian.
