Victim Fares Maatou was set upon by the two boys after a confrontation with a larger group in Canning Town, east London, on April 23 last year, prosecutor Julian Evans QC alleged.
The Metropolitan Police said at the time Fares was found seriously injured outside a pizza restaurant.
The two defendants, who cannot be named because of their age, deny murder.
The now-16-year-old teenagers say they were acting in self-defence.
Mr Evans told the Old Bailey the schoolboy “offered no threat at all”.
He said: “He was unarmed.
“He displayed no aggression towards them.”
Jurors heard Fares suffered a single 11cm (4.3in) injury to the left side of his upper back, caused by the sword, which had been stolen from the grandfather of one defendant, then aged 14, and passed to the other defendant, then aged 15.
The then 14-year-old beat Fares with the sheath, jurors were told, before both youths fled the scene.
Prosecutor Mr Evans told the court the attack, on Barking Road, was caught on CCTV footage.
He said: “Both of his [Fares’] hands were in front of him at waist height. Fares was not holding anything. He was completely unarmed.”
The older boy then lunged at Fares — the first of three such attempted blows with the sword — while the younger boy swung the sheath, the jury was told.
The weapon they used, Mr Evans said, would “look like a walking stick” to passers-by.
The prosecutor said: “Fares reacted by bringing both of his hands up towards his face and head to protect himself.
“As he, Fares, tried to escape, he turned his back on (the defendants) and he, Fares, moved away.
“Despite that action, (the defendants) continued to attack him.”
Fares tried to run away but slipped, and the defendants continued to attack him, the jury was told.
The victim briefly managed to get to his feet once the attack stopped, the court heard, but he lost his footing again and fell against a parked car nearby.
Paramedics and an air ambulance attended the scene but despite medical treatment, the boy was pronounced dead at the scene.
The trial continues.