A Lamborghini clocked by police driving at high speed crashed moments later and burst into flames.
The green hire car was seen by road policing officers on Wakefield Road, Bradford, at 22:30 GMT.
It crashed into a parked VW Golf, with a motorist sat inside, which in turn hit an unoccupied parked Kia.
The Lamborghini driver, a man aged 25, suffered head injuries. His female passenger, also 25, and the male Golf driver had minor injuries.
West Yorkshire Police said the traffic officers were conducting static speed enforcement checks on the road, which has a 40mph limit and is known locally as a hotspot for speeding.
The force said the incident had been referred to the Independent Office for Police Conduct, which attended the scene on Saturday evening.
The officers were not in pursuit of the vehicle at the time of the crash and ran on foot to the scene to give first aid, the force added.
