Daniel Graham was attacked by up to six people "in full view" of the passengers on a bus and pedestrians in East Dulwich early on Saturday, they added.
It is believed he was chased down a hill after a mass brawl at a party.
The 14-year-old was attacked in a supermarket car park nearby. A boy of 13 has been bailed until late March.
Police said Mr Graham had been at a party at Dulwich Hamlet football club on Friday night.
About 70 youths were ejected from the clubhouse when the celebrations turned rowdy, witnesses said.
Mr Graham, from Peckham Rye, left the party and ran down Dog Kennel Hill before boarding a stationary 176 bus.
But when he realised he was being followed, he got off the vehicle, police said.
He was then stabbed several times in the street at 0020 GMT.
He managed to board the bus again, at which point passengers rang for an ambulance, but he died in hospital two hours later.
Separately the 14-year-old victim, whose identity has not been given, was found at a hospital where he was seeking treatment for a gunshot wound to the leg.
He remains in a stable condition.
"East Dulwich is a busy area on a Friday night and I am sure that many people witnessed both incidents," said Det Ch Insp Dave Manning of the Metropolitan Police.
"I need to hear from any of the passengers on the 176 bus or any pedestrians who were in the vicinity to come forward."
He is the fourth teenager to be murdered in London in 2011.
"Many people" will have witnessed the fatal stabbing of an 18-year-old and the shooting of a boy aged 14 in south London, police have said.