Police spotted the stolen car driving in Harold Road towards the Old Town at 9.40pm and turned round to give chase.
The silver Mondeo overtook a four-wheel drive vehicle and was in the middle of the road at the brow of a hill before colliding with a Vauxhall Zafira people carrier travelling in the opposite direction.
Peter Pearce, of Harold Road, came out of his house when he heard the crash.
He said: "It was one hell of a bang. Half the Mondeo was written off and the engine was totally dislodged and pushed to one side. The passengers in the people carrier seemed to be traumatised."
Firefighters from The Ridge and Bohemia arrived on the scene in five minutes and sealed the area off. They cut the driver out of the people carrier and stayed on the scene for about one-and-a-half hours. The road was sealed off for three hours.
The Ridge sub-officer Paul Evans said: "Both cars were leaking quite a bit of fuel and there was a lot of debris everywhere and people wandering around injured."
The Mondeo had been used by a man and a woman who were reported as having shoplifted and assaulted staff in Bexhill Sainsbury's last Friday. The car was also used in a shoplifting offence in Rye on Monday.
The male driver and female passenger in the Mondeo were both taken to Conquest Hospital before being taken into custody at Hastings Police Station in connection with the theft in Bexhill and the stolen Mondeo.
A group of five holidaymakers from Guildford, Surrey, was in the Zafira. All five, four women and one man, were taken to Conquest Hospital with injuries. One woman was still in hospital at the time of going to press with a suspected fractured hip.
The rest of the group checked out of Shearbarn Holiday Park on Tuesday night.
The Police Complaints Authority is investigating the incident, as is standard procedure when police are involved in a car crash.
Police are appealing for anyone with information about the crash to call them on 0845 6070999.