Omid Saidy, 20, was heard screaming for help as he lay injured in the road outside Parsons Green station in west London on Monday evening.
He was treated by medics but died at the scene in front of distraught family members who had raced to be by his side.
Scotland Yard said Mr Saidy, from Fulham, confronted a drug dealer and another man and asked them to move on before he was attacked.
He chased the two suspects along Beconsfield Walk and was stabbed when he caught up with them, police said. Mr Saidy was pronounced dead in Parsons Green Lane at about 8.30pm.
A witness, who did not want to be named, told the Standard: “He was shouting help for ages when he was lying on the floor. His brother and sister turned up and were trying to help.
“I heard someone say ‘he’s breathing again’, then about ten minutes later I heard screaming, ‘he’s dead, he’s dead.”
Mr Saidy’s friend, a 20-year-old man, came to his aid, arriving in the street on a moped and was also knifed. His moped crashed into a parked car, Scotland Yard said.
He remained in hospital on Tuesday evening. His injuries are serious but not life threatening.
One of the suspects, a black male dressed in dark clothing, fled down Harbled Road towards Fulham Court.
A second suspect, a 16-year-old boy who is described as a white male youth, also suffered stab wounds and was taken to hospital.
He has since been discharged from hospital and arrested on suspicion of murder and attempted murder. He was taken to a west London police station where he remained on Tuesday evening.
Detective Chief Inspector Noel McHugh of the Met’s Homicide and Major Crime Command who is leading the investigation said: "At this early stage we are piecing together a picture of how the sequence of events leading to and immediately following the murder took place.
"It is imperative that we speak to anyone who was in the area of Parsons Green station between 7pm and 8pm who may have witnessed the murder or the actions of the suspects immediately following the incident.
"In addition, I am keen to identify the black male who fled Parsons Green Lane immediately following the murder and am appealing for footage that members of the public may have recorded as events in the area took place.
"A young man has tragically lost his life for simply asking a drug dealer to move on. I urge anyone who can assist our investigation to come forward without delay."
Anyone with information is asked to contact police on their incident room number of 0208 785 8099 or to remain anonymous please call Crimestoppers on 0800 555 111.