The 66-year-old formally pleaded guilty in Melbourne Magistrates Court yesterday.
Mathieson met his victim in 2020 when they were walking their dogs and the pair struck up a friendship, the court was told.
On March 13, 2022, the woman invited Mathieson over for dinner at her Brunswick East home and the pair drank wine before watching a Whitney Houston documentary on her lounge and falling asleep.
The woman woke up to see Mathieson sucking on her nipple while he cupped her breast with his hand.
When she told Mathieson "don't do that" and pushed him away, he kept trying to put his mouth back on her breast before she ordered him to get out.
The woman confronted Mathieson about his behaviour the following day and he laughed at her before saying, "that won't happen again".
She reported the assault to police 10 days later.
The woman moved interstate within weeks after feeling unsafe in her home and afraid Mathieson would come back.
The attack came after she made it clear to him she didn't want more than a friendship, she said.
"I felt like the friendship was a lie and I had not been heard," the woman said in a victim impact statement read aloud to the court.
"I was in a state of confusion, anger and feeling completely disrespected."
The woman said she dealt with an eating disorder along with anxiety and feelings of distrust - particularly towards men - after the assault.
The interstate move took a toll on her work and she ultimately relocated overseas to have her family's support and feel safer, she said.
Mathieson's barrister Brad Penno pushed for his client to be spared a conviction, noting his remorse and unclear recollection of the assault.
He initially denied the attack and told police he and the woman fooled around on the couch kissing and cuddling before they fell asleep.
Mathieson now remembered the incident as "involving affection and cuddling" and regarded his relationship with the woman as close and intimate after they spent time together at both their homes and kissed, Mr Penno said.
However, it was clear the victim was not interested in an exclusive sexual relationship with him, the barrister said.
Magistrate Belinda Franjic said the assault was serious.
"It's a particularly intimate form of sexual assault," she said.
"He made a decision to take advantage of a sleeping friend ... (and) when she attempted to push him away, he continued to try to get his mouth back on her breast."
In March 2022, Ms Gillard told the Adelaide Advertiser the couple had broken up about 18 months earlier.
She and Mathieson, a former hairdresser, were together for a decade and lived at The Lodge and Kirribilli House throughout Ms Gillard's three-year term as prime minister.
During that time, Mathieson was dubbed "Australia's first bloke".
Mr Penno on Thursday said his client, "a talented and creative hairdresser who made an impression", met the former prime minister in 2004.
Their relationship was impacted by the COVID-19 pandemic after Ms Gillard was given a posting in London.
Ms Franjic noted the incident was completely out of character for Mathieson, who - according to his barrister - enrolled in a men's behavioural program after the assault.
Mathieson refused to comment as he left the court.
