The so-called "Hanoi burglary" took place on Kemp Road in Swanland, East Yorkshire,
The home was broken into sometime between 10pm on Wednesday and 5am on Thursday.
A purse and keys were stolen, which were then used to take a grey BMW 5 series and a blue BMW X5 from outside the premises.
The grey BMW was later found on Southwood Road in Cottingham after it had crashed into two cars and a telegraph pole.
The X5 was recovered later in Hull city centre.
Detective Chief Inspector Jon Cross said: “Investigations are ongoing and we are very keen to find those responsible for this burglary and the subsequent theft of two vehicles.
“Having your home burgled is an awful experience that leaves victims violated and vulnerable. It is one of our main priorities for our teams across Hull and the wider area who are working together on intelligence, enforcement and prevention.
“The public’s role in preventing burglary is vital. We also want the public to call us to let us know about crimes in progress or people responsible. I would urge people to help by keeping their homes locked and secure to prevent burglaries – a quarter of which are a result of insecurities."
Hanoi burglaries involve the culprits stealing a vehicle after the break-in.
Anyone with information is asked to contact 101, quoting log 44 of January 4.