Mohib Tasharat, Kasim Ifzaal and Ibrahim Raza were among a group of men who chased and killed Bashir Mohamed in the early hours of April 22 last year.
Mr Mohamed was pursued by cars through Birmingham and then chased on foot before being stabbed in the arm and bleeding to death at the scene in Ladywood.
Through CCTV and other inquiries, West Midlands Police quickly identified 24-year-old Tasharat and 26-year-old Ifzaal as being among the attackers.
Tasharat, from Wenlock Road, tried fleeing the UK for Pakistan the following day but officers detained him at Birmingham Airport before he could board a flight.
Ifzaal, from Ombersley Road, was arrested three days later in Dover as he drove towards the port where he intended catching a crossing to the Continent.
The investigation by West Midlands Police led to the arrest of 32-year-old Raza on May 10 from his home in Oldfield Road in Birmingham.
They were charged with murder, but following lengthy deliberations at Birmingham Crown Court, the jury were unable to reach a verdict.
All three admitted manslaughter and Tasharat, Ifzaal and Raza were jailed for 11, 10 and six-and-a-half years respectively during sentencing on Friday.
A fourth man, Nabil Akhtar, was cleared of involvement in the killing.
The force said it believes three other men were involved and fled the country just hours after the killing and are working to find them and bring them back to the UK.
Detective Inspector Laura Harrison from the Homicide Unit said: “There was clearly some kind of dispute between two groups, which we believe escalated when a car deliberately rammed into a dessert shop in Ladypool Road last May.
“We believe that prompted the arson attack on the house in Fulham Road and the shocking fallout from that which saw Mr Mohamed chased and fatally stabbed.
“These men pursued the victim for several minutes in cars and were determined to cause him serious harm.”
A 27-year-old man suspected of petrol bombing the house in Fulham Road before the stabbing is due to stand trial for arson and gun possession at a later date.