The maintenance driver can be seen leaping from the 66ft train at Highgate tube station after its brakes failed.
The worker puts his hands on his head as the train hurtles off into the London rush hour.
Passengers can be seen in one frame waiting on a packed platform at Archway station as the train speeds past.
A train in front of it was told to keep going and not stop, while its passengers were told to run to the front carriages, the Old Bailey heard.
London Underground, Tube Lines Ltd and Schweerbau GMBH pleaded guilty to endangering passengers and staff under Health and Safety law. They were each fined £100,000.
Tube Lines and LU are part of Transport for London while the German company manufactured the wagon and its tow-bar.
Judge Richard Hone said: “There was the potential of terrible tragedy.”
He said the runaway train was out of control for four miles during 16 minutes.
“To those involved it must have seemed an extremely frightening eternity,” he added.
The court was told that a fault had now been remedied and the incident was extremely unlikely to occur again.
Jonathan Ashley-Norman, prosecuting for the Office of Rail Regulation, told the court that the rail grinding unit was being towed when it broke away during the early morning.
It started rolling downhill without brakes from Highgate and into central London in August, 2010.
“It could have led to tragedy but thanks to the immediate actions of LU staff, no one was hurt,” said Mr Ashley-Norman.
Speeds of 30mph were reached as it raced after the passenger train which was told to speed out of the next station at Archway, north London, and to keep going.
Control staff watched helplessly as they saw the flashing lights of both vehicles turn into one as the grinder got within 600 metres of the fleeing train.
Mr Ashley-Norman said attempts were made to slow the runaway train down using points at Camden Town and Mornington Crescent, and the trains were diverted onto different lines.
It eventually stopped at Warren Street central London when it reached an upward incline.
“In the event, and fortunately, no-one was harmed,” added Mr Ashley-Norman.
Keith Morton, QC, for the Tube companies, said: “London Underground is one of the safest railways in the world - if not the safest.”
He said a billion passenger journeys were made on London’s Tube network each year.
