Emergency services were called at around 8pm on Sunday when the vehicle smashed into the home in Cottingley Drive, Cottingley.
The Vauxhall Corsa had collided with a Toyota Avensis taxi before careering off the road.
Police and firefighters were joined by members of Yorkshire Ambulance Service's Hazardous Area Response Team, which provides advanced critical care, support and rescue.
Representatives from Transco and National Grid were also called upon after it emerged the crash had ruptured a gas pipe and affected power supplies to neighbouring homes.
A number of properties in the area were evacuated while emergency teams were called in to make the area safe and residents were only able to return home when a cordon was lifted at about 10.30pm.
An ambulance service spokeswoman said: "A gas pipe was damaged as a result of the collision and our Hazardous Area Response Team remained on scene for 2.5 hours as a precautionary measure while the area was made safe for local residents.
"No patients were treated on scene or conveyed to hospital."
Police said the occupants of the Corsa ran away from the scene.
A spokesman said said: "It was established that the Corsa had been stolen earlier in a burglary and enquiries are ongoing into the offence."
He said nobody was injured but the taxi had been damaged during the initial collision.