The incidents happened in Barnsley.
The first, in Darley Avenue, Athersley South, was reported at about 11pm. The fire damaged the gas supply to a nearby home, so safety engineers also had to be called out.
The second was started in Princess Street, Staincross, just before 6am. Firefighters said the flames had cut through the brakes and caused the car to roll down the hill, crashing into a telegraph pole.
No-one is thought to have been hurt.