The 1949 Delahaye Roadster, which some have dubbed the most beautiful car in the world, was given to Dors when she was 17.
The sky blue car has been described by auctioneers as "extravagant and outrageous - a rolling sculpture".
Dors, who was seen as the British Marilyn Monroe, died in 1984 aged 52.
Born Diana Mary Fluck, Dors became known as a 1950s blonde sex symbol, but was also well-respected for her acting skills.
RM auctioneers said the car was curvaceous, sexy and flamboyant, just like its former owner.
It was expected to sell for up to $6m but went for $3m plus a buyer's premium of 10%.
The car is one of only 150 Roadsters made, and only one of 51 of its specific model - the 175S.
The company stopped production in 1951 as it found there was little demand for such extravagance during that post-war period.
When Dors first received the car, she did not even have a driving licence.
At 20, she became the youngest owner of a Rolls-Royce in the UK - a reflection of her success at an early age.
After she died, the car changed ownership several times and has in recent years been restored to its former condition.
In its catalogue listing, RM Auctions says the Roadster - which has a top speed of 70mph - can "easily claim to being the most extravagant and beautiful coachbulit car in existence".

It bought the Grade II listed building for £225,000 in the summer.
The Guildhall had been facing uncertainty after the Ministry of Justice announced it was one of 10 law courts to close in Wales.
The council said it was still investigating how to make best use of the venue.
Carmarthenshire council's deputy leader and executive board member for resources, David Jenkins said one of the main reasons for buying it was to "ensure a secure future."
He said it was a "focal point" not just for Carmarthen, but for the whole county.
"It has a tremendous history. Murderers have been tried and condemned to death here."
They include Ronnie Harries, who was one of the last men to be hanged in Wales. He was sentenced to death in 1953 after murdering his relatives Phoebe and John Harries at their home in Llangynin, Carmarthenshire.
The Guildhall was also the setting for Gwynfor Evans' landmark victory as first Plaid Cymru MP in 1966.
Mr Jenkins admitted when the Ministry of Justice announced the building was to be sold, they were hoping "to pick it up for a £1," but ended up paying the district valuer's price tag.
The council is now speaking to potential partners, including Carmarthen Town Council and Dyfed-Powys Police, about the building's future.
"We've got ideas of bringing some of our own services in here," said Cllr Jenkins.
"It'll also be good as a museum. We could bring people inside just to see how beautiful it is.
"The intention is to make the building self sufficient."

Media playback is unsupported on your device
19 November 2014 Last updated at 08:38 GMT
It follows a BBC investigation into how assembly members use their expenses.
Ciara Riddell reports.

The 27-year-old man from Blackburn was riding a grey Triumph Daytona motorcycle along the B6479 near Selside when he crashed at 19:25 BST on Wednesday.
The air ambulance was called but the biker died at the scene.
The road was closed for five hours to allow collision investigators to examine it.
A sports car once owned by the late British actress Diana Dors has sold for $3 million (Â£1.9m) at a California auction.
[NEXT_CONCEPT]
Carmarthen's Guildhall has a "self sufficient" future say council leaders, as the county takes ownership of the historic building.
[NEXT_CONCEPT]
The former chairman of a Westminster standards watchdog has called for an investigation into societies that receive public money in rent from MLAs for their constituency offices.
[NEXT_CONCEPT]
A motorbiker has died after hitting a sign at the side of the road in North Yorkshire.