Kevin Nguyen and Milumo Pedrinho, both 21, chased 33-year-old Ervin Baraku into the station as he fell down the stairs and was stabbed in the chest.
Baraku was rushed to hospital, where he died a week later on July 30.
Nguyen, of Westerfield Road, was sentenced on Thursday (July 28) to life imprisonment with a minimum term of 18 years, having been found guilty of murder at Inner London Crown Court on June 12.
Pedrinho, of Stonebridge Road, has also been sentenced to life imprisonment, but with a minimum term of 17 years, after pleading guilty on April 24.
The court heard how the two were in the area when Nguyen had an altercation with the victim on the street.
Screaming and shouting could be heard as Ervin was chased into the station by Pedrinho who was seen with a large knife on CCTV, being followed by Nguyen.
Pedrinho and Nguyen fled the station after the stabbing, while Ervin collapsed at the top of the stairs.
Nguyen was arrested the next day by British Transport Police officers at his home address.
Pedrinho was arrested only a few days later on July 27 last year.
Detective Superintendent Sam Blackburn said: “This was an absolutely senseless and tragic attack that resulted in a father, a brother, and a son losing his life.
“The actions of Pedrinho and Nguyen will forever leave a devastating hole in the lives of Ervin’s family and friends, so I am pleased to see them both receive a significant prison sentence for their barbaric actions that day.
“While no prison sentence can ever make up for the loss of a loved one, I hope justice being served can bring Ervin’s family some peace after this horrific ordeal.
“I also hope the sentence serves as a reminder that there will never be a place for violence on the railway network, and we will continue to do everything we to ensure dangerous offenders are held to account.”
