The court heard that Pagani, from Dumfries, initially blamed someone else but later admitted the offence when her finger prints were found on the bottle.
Alan Lovett, prosecuting, said she had been in Carlisle celebrating her birthday when the incident occurred in December.
“In the bar there is a dance floor area,” he said. “Both groups were dancing on the dance floor when a scuffle broke out.
"While being escorted out of the bar by door staff the defendant picked up a bottle and threw it over her shoulder across the crowded dance floor in the direction of the other group.”
In mitigation, Alison Whalley, defending, said Pagani had received a good education and intended to continue working as a hairdresser should she avoid custody.
She also cited Pagani's lack of self-esteem, her past record of self harm and her successful figure skating career.
But Pagani, dressed in a leopard skin coat, wept in the dock as Judge Barbara Forrester sentenced her to eight months in a young offenders institute.
"The injury could have been far worse,” the judge said.
"Anyone who throws a bottle into a crowd of people is likely to cause serious injury.
"I have thought about this for some time. This offence took place in a licensed premises when people were out enjoying themselves.
"For no reason you threw a bottle over your shoulder.
"You had no concern over the injury it would cause. It caused serious injury and could have been even worse.
"This behaviour is totally unacceptable. It quite clearly passes the custody threshold."
Pagani represented Great Britain in the prestigious Trigalev Trophy in Slovenia and was considered to have "tremendous potential".
Her father John, a good friend of Scottish actress Ashley Jensen, is a wealthy business tycoon in south west Scotland.
A friend of the family, who asked not to be named, said: "It's such a shame.
"You see a lot of cases of young people being jailed after being brought up in terrible backgrounds where they never had a chance.
"But Rachel is a girl from a wealthy background who has had a lot of opportunities. It really is unbelievable.
"She was a very good skater, very talented."