Nathan Gilmaney, 19, and Troy Thomas, 18, killed youth worker Abdul Samad for his iPhone as they swept across London in a spree of “aggression and blood lust”, the Old Bailey heard.
The teenagers robbed a total of nine people, stabbing four of them, in a matter of hours.
They were dubbed “highwaymen of the 21st century” by prosecutors.
The pair continued to search for victims as Mr Samad collapsed on his doorstep in front of his horrified parents.
CCTV footage shows the teenagers, on a moped with the plates removed, pursuing a clearly terrified pedestrian through an empty west London street later in the evening.
It is understood that Gilmaney stabbed his victim in the chest in an attempt to take the PIN code for his phone.
He was sentenced to life imprisonment with a minimum of 27 years, while Thomas was sentenced to a minimum of 22 years.
Judge Richard Marks QC described 28-year-old Mr Samad as an “outstanding” young man, engaged to be married and “with his whole life ahead of him”.
“Your wicked stabbing of him has left his family understandably utterly devastated,” he said.
Mr Samad’s girlfriend, Sultana Ahmed, described him as the “change we needed to see in the world” and said the last thing he said to her was: “This year will be our year and we will be a family”.
His mother Layla Begum said the family had been “broken” by the murder, on 16 October last year.
“Since his death there has not been a single moment that goes by for me without shedding tears,” she said.
Detective Inspector Shaun Fitzgerald said the teenagers could hear Mr Samad’s cries and the paramedics giving him surgery in the street, but sped off on Gilmaney’s scooter to continue their spree.
They were caught by police officers on the same night.
“The teenagers believed they had the right to threaten and rob wherever they wanted, often stabbing their victims for no reason at all but to prove they could,” DI Fitzgerald said.