Courtney Ridgeway carried out the attack after the two women fought with each other during a dispute at a supported housing complex in Leeds.
Leeds Crown Court heard the incident took place on December 27, 2019.
Lucy Brown, prosecuting, said the victim and Ridgeway's brother were residents at the premises.
Ms Brown said Ridgeway and the woman had known each other for around seven months and had previously got on well.
Shortly before the incident the victim went outside to have a cigarette where she saw Ridgeway, Ridgeway's brother and another woman having an argument.
The victim asked Ridgeway to leave before punching the defendant, causing a split lip.
Ridgeway retaliated by grabbing the woman by the hair and the pair began fighting.
Staff at the premises intervened and stopped the fight.
The victim was led away to her bedroom by a duty care worker.
Moments later Ridgeway burst into the room and the care worker stood between them in an attempt to stop further violence.
The prosecutor said Ridgeway then struck the victim to the side of the head with a broken Champagne flute.
She instantly felt pain and began bleeding.
A witness later described how Ridgeway had picked up the glass and smashed it against a wall before carrying out the attack.
The wound was so deep that the victim's skull was visible.
Police were contacted and they recovered the broken Champagne flute.
Ridgeway's and the victim's DNA were found on the weapon which indicated that it had been used to carry out the attack.
Officers arrested Ridgeway at her then home in Gipton.
The defendant told the officers: "You should be locking her up too.
"I have spoken to her on the phone and we are all sorted now."
The victim suffered a 5cm deep cut near to her temple which had to be cleaned and X-rayed.
She provided a statement to the court describing how she has been left permanently scarred.
Ridgeway, 21, of Cavalier View, Cross Green, Leeds, pleaded guilty to unlawful wounding.
Michael Walsh, mitigating, said Ridgeway was aged 19 at the time of the offence and had not been in trouble since.
Mr Walsh said his client carried out the attack "in the heat of the moment" after being provoked.
He added that Ridgeway is now doing an art and design course at college and works part time for a food retailer.
Ridgeway was jailed for two years and 11 months.
Judge Tom Bayliss QC said: "What caused the fight and why you were fighting is immaterial.
"It was broken up and a duty care worker took (the victim) back to her flat.
"Unfortunately, you were not for giving up the fight.
"You burst into the bedroom. You broke a Champagne glass, as you acknowledge you did, and you struck her in the face with the broken glass.
"I am satisfied that since the offence you have tried to put it behind you.
"But I am afraid to say that I take the view that it is inevitable that there has to be a custodial sentence in this case."