The victim got in to his car after the incident in a stairwell on Wardieburn Street West and drove to nearby Wardieburn Place West.
A passer-by then raised the alarm before the 45-year-old and the second victim were rushed to hospital.
The driver is in a critical condition while his companion has serious injuries. Both suffered stab wounds from a “sharp instrument”.
They were attacked within a common stair in Wardieburn Place West at around 6pm yesterday by two male suspects, who quickly departed the scene, possibly via the large grass area at the rear of the block.
The victims are understood to have come down from Aberdeen to buy a car.
Officers are now eager to speak to any witnesses who may have seen the two suspects.
The first is described as a white man, aged between 17 and 19 years old.
He is said to have a Central Scotland accent and light coloured short hair, which is shaved at the sides.
He was also wearing a light coloured sky-blue hooded sweatshirt and grey jogging bottoms.
The second suspect is a white man in his mid-twenties. He has a stocky build and was wearing a striped top.
Detective Chief Inspector Stuart Houston said: “This was an appalling attack on two men who came to the address in good faith.
“This attack happened in daylight and we believe there may be a number of witnesses who may have seen the suspects in the area.”
A local resident said she was horrified to return home last night to find the street completely blocked off by police.
The woman, who asked not to be named, said: “A few years ago there was a stabbing just along the road.
“It’s a shame. There have always been antisocial behaviour concerns, you hear noise of people coming home from the pub, but you don’t expect this to happen, not on your doorstep. When things like this happen close to home, it makes you think.”
Anyone with information is asked to call police immediately on 101.