Alan Morton, 38, of Edinburgh, based at Sighthill Fire Station in the city, was answering an emergency call in Tollcross on 28 December 2005.
Aisling Bateman, 24, of Edinburgh, raised a civil action against Mr Morton at the city's sheriff court.
Sheriff Elizabeth Jarvie found the collision was caused by his negligence.
As Mr Morton drove his vehicle along Gorgie Road towards the crossroads with Gorgie Park Road and Westfield Road, the lights turned to red against him.
There were several vehicles stopped in front of the fire appliance and he moved into the lane for oncoming traffic, which was empty, and drove through the red light onto the junction.
Crashed into railings
Ms Bateman had been driving along Gorgie Park Road in her Citroen car and had stopped at the junction.
When the lights turned green for her to proceed, she did so at between 15mph and 20 mph.
A passenger in her car screamed and the fire appliance, travelling between 25mph and 30mph, struck Ms Bateman's car, knocking it into another vehicle.
The fire appliance crashed into railings in Westfield Road.
Sheriff Jarvie said Mr Morton had breached his duty to treat the red light as a "Give Way" sign, to keep a proper lookout for traffic in Gorgie Park Road and to drive at a speed which would have allowed him to give way to Ms Bateman's car.
She also held the siren of the appliance had not been activated in time to alert Ms Bateman and there was nothing she could have done to avoid the collision as her view at the junction was obscured by a high hedge.
The court heard that the fire crew was not answering a high priority call but were acting as a back-up to the Tollcross crew.
The blue lights were switched on but the siren was being used "from time to time".
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