Former boxer John Laidlaw, 24, went on a shooting spree in Islington, north London, last May, the Old Bailey heard.
It is not clear whether the attacks were related to his threats against black people.
He shot Abu Kamara in Upper Street before accidentally shooting Emma Sheridan at Finsbury Park Tube station, as he aimed at a second man.
Laidlaw, from Holloway, north London, was also found guilty of two firearms charges.
Judge Samuel Wiggs warned him that he faced an indeterminate jail sentence for the public’s protection.
“These offences, certainly the first incident, seem to be almost completely random,” he said.
Detective Sergeant Nick Bonomini, of Scotland Yard’s Serious Crime Directorate, said: “He has previously demonstrated a high level of aggression towards black people that appears, given his words, to be based on their race.
“But there was no evidence in these current two shootings that suggest that this formed the same sort of motivation for him and on that we have an open mind.”
Social worker Mr Kamara, 44, had been with a group of work friends going for a drink after a game of badminton.
When a sports bag belonging to one of his colleagues brushed against a friend of Laidlaw’s, the gunman reacted by pulling out a gun and shooting Mr Kamara.
The bullet was deflected off Mr Kamara’s chin and entered his neck through his Adam’s apple.
It went through his voicebox before finally lodging near his spinal column.
Half an hour after shooting Mr Kamara, Laidlaw shot at a man called Evans Baptiste.
Mr Baptiste and a friend had been chasing Laidlaw after recognising him as the man who had attacked Mr Baptiste with a hammer earlier in the year.
But the bullet brushed past Mr Baptiste and struck 26-year-old Emma Sheridan in the back.
A passing medical student plucked the bullet from her back before ambulance crews took her to hospital for treatment.
When police caught up with Laidlaw at the home of a family friend in Kingston, south-west London, he dived through a glass door and ran into a shed to hide.
n court, he claimed he was watching television all day during the shootings and was the victim of mistaken identity.
Three weeks before the shooting spree, Laidlaw admitted in court attacking a black motorist.
When he was arrested he behaved violently and was “foaming at the mouth” according to a police document.
“In the presence and hearing of the black female jailer the defendant made racist comments and remarks, stating he was a member of the BNP and that he hated all black people,” the document says.
He also stated that he was going to kill all black people, said the report.