Prosecutor Mark Ellison QC outlined to a jury how modern forensic techniques were used to detect the traces more than a decade after the 18-year-old’s murder.
Mr Lawrence was stabbed by a gang of white youths at a bus stop in Eltham, south east London, in April, 1993.
Gary Dobson, 36, and David Norris, 35, both of south-London, deny the murder.
A cold case review was started in 2007 during which forensic experts re-examined clothing seized as part of the original police investigation.
Mr Ellison said that new evidence was found that “consists of the finding of textile fibres, blood and hair linked to Stephen Lawrence on clothing seized from the defendants as part of the original investigation in 1993”.
The court was told that a tiny bloodstain found on Dobson’s grey jacket was a billion-to-one match to Mr Lawrence’s DNA. Mr Ellison said some of the blood on the collar had soaked into the fibres, suggesting it had been wet and had come from the attack.
There were also minute flecks of blood on the jacket itself which had been found by microscopic examination. These did not contain a full DNA profile.
In total there were 16 fibres which could have come from three separate items of clothing worn by Mr Lawrence, found either on the jacket or its bag, the jury heard. Two hairs were found in an evidence bag used to store Norris’s jeans, one of which was 2mm long and was found to match Mr Lawrence’s DNA to a certainty of one in 1,000.
A total of seven fibres were also found on Norris’s sweatshirt which potentially came from two items of Mr Lawrence’s clothes, the jury was told.
Earlier, the court heard that the 18-year-old student was attacked after being surrounded by a group of white men as he and his friend, Duwayne Brooks, waited for a bus.
Mr Ellison said: “One of the group was heard to say ‘What, what nigger?’ and at the same time the whole group rushed towards them.” Mr Brooks managed to run off after shouting: “Get up and run, Steve.”
But, Mr Ellison continued: “Stephen Lawrence did not manage to get away. The group quickly surrounded him. One witness described that he was swallowed up by the weight of numbers and forced to the ground.”
Medical evidence suggested one of the two stab wounds to his torso was inflicted when he was standing, the other when he was on the ground.
Defending Dobson, Timothy Roberts QC told the jury that the clothing had been contaminated while in police custody and the evidence amounted to only “a teaspoon”.
The trial continues.