CCTV footage shows the attackers repeatedly punching and stamping on female goth Melody McDermott's head on a Metrolink tram.
Kenneth Kelsall, 47, of Cornwood Close, Cheetham Hill, was sentenced to six years nine months in prison at Bolton Crown Court and Gareth Farrar, 43, of Ellingham Close, Beswick, for two years two months.
Kelsall pleaded guilty to causing grievous bodily harm with intent and assault occasioning actual bodily harm at a previous hearing.
Farrar pleaded guilty to assault causing actual bodily harm.
Sentencing, Judge Elliot Knopf said: "This was an explosion of violence against two young people. The CCTV recording speaks for itself and demonstrates the value of CCTV in assisting the courts in getting to the truth."