Sean Gorman, 18, repeatedly stabbed Mr Ali in a frenzy at a hostel in Upper Gilmore Place in the early hours of May 3.
Family of Mr Ali welcomed the sentence after Gorman was jailed for more than eight years yesterday.
Family lawyer Aamer Anwar said: “Shabaz’s father welcomes the significant sentence imposed today by Lord Woolman and the message sent out to violent racists like Sean Gorman.”
Gorman went berserk with a lock knife after Mr Ali, 25, asked him and his friends to turn their music down as he had work as a barber in the morning.
A court heard Gorman was “hyper” after downing much of a litre bottle of vodka and taking ecstasy and cocaine prior to the unprovoked attack.
He later told social workers: “Deep down, I think I did want to stab somebody.”
Gorman, who last month admitted to the racially-aggravated murder bid, returned to the High Court in Edinburgh for sentencing yesterday.
Judge Lord Woolman handed him an extended sentence of 11 years and nine months, involving detention for seven years and nine months followed by four years of supervision upon his release from custody.
Gorman was also ordered to start that sentence when he had finished serving 169 days of the previous sentence from 2017 for assault to severe injury and the danger of life.
The judge told the 18-year-old: “You carried out a frenzied attack on a stranger, Mr Shabaz Ali.
“You stabbed him six times – five times in the upper chest.
“But you would have been a threat to anyone you came across that night.”
Aspiring engineering student Mr Ali was left fighting for life after the attack and will still need multiple operations to walk again.
The court was told the attack had caused Mr Ali serious physical and psychological harm as well as having a profound effect on his family.
Lord Woolman warned the attacker: “Without the urgent and expert hospital treatment he received, you could have faced a charge of murder.”
Mr Ali fled to Scotland five years ago with his relatives after nine of their family were butchered by ISIS. He was working as a barber and staying in the hostel temporarily as he looked for a new home.
It is believed Mr Ali still wants to pursue an engineering career in the UK despite the horrific ordeal.
Mr Anwar repeated claims Mr Ali had been repeatedly let down by the city council after he reported fearing for his life in the days leading up to the attack. But a council spokesman said: “We welcome the sentence handed down today by Lord Woolman for what was a despicable attack.
“The council and our partners have provided and continue to provide significant level of tenancy support and guidance to Mr Ali and his family, including previous offers of alternative accommodation.
“Anyone who is assessed as homeless is supported to find settled or permanent accommodation and at no point has Mr Ali been refused this.”