Police are investigating exactly how the car managed to "take off" from street level and crash into the house in Basingstoke, Hants, on Wednesday.
The men's condition is described as serious, but stable. Police want to speak to a third man, who was helped from the car but then left the scene.
The occupants escaped uninjured as they were asleep in another bedroom.
A police spokeswoman said that one man was found in a passenger seat and the other man, who they believe could be the driver, was found under the front wheels.
Joyce Harman told BBC News how she and her husband Joe were woken by the crash.
"It was just horrendous," she said.
"My husband thought the dog had knocked something over downstairs but as he got to the bedroom door he could see the hole in the wall and all the furniture moved.
"That's when we came downstairs and saw the car there."
The Harmans have been told they will not be able to live in their home for at least two months and that it will have to be partially rebuilt.
The damaged room was their study, which used to be their children's bedroom.
The couple's neighbour, George Harrison, said what had happened was "just absolutely incredible."
"The fence has been knocked down and the car's gone through a pathway, a signpost, a tree and the front lawn.
"How this happened I shall never know."
A Hampshire Police spokesperson said the red BMW lost control on a bend of the nearby A30, hit the kerb and "launched through the air, colliding with the first floor of a house in Rainbow Close."
"A full investigation has been launched into the circumstances of the crash and how the vehicle collided with the first floor," she said.
Officers have not yet dismissed reports that a third person may have been driving the car.
They are trying to trace the vehicle's registered owner, but it was not reported stolen at the time of the crash.
The injured people have not been named.