The daring officers, who were later treated in hospital for smoke inhalation, rescued the occupant from the fourth-floor flat in Pilrig Heights after a "significant" blaze broke out in his living room at 2.45pm.
Around 20 firefighters tackled the fire for about 40 minutes before making the property safe. The male occupant was taken by ambulance to Edinburgh Royal Infirmary "conscious and breathing" having suffered smoke inhalation.
Fire crews from McDonald Road and Marionville extinguished the flames while a height appliance from Crewe Toll also attended.
"When we got to the scene the living room was well alight and we had six firefighters battling the flames there," said a spokesperson for Lothian and Borders Fire and Rescue Service.
"The police have done a very good job here. They managed to get him out of the property in time and he was taken to hospital by ambulance for treatment for smoke inhalation."
She added: "The fact that we were using as many as six breathing apparatus for this incident suggests it was a significant blaze and shows there was a concern it could spread."
The cause of the fire is still unclear but a fire investigation team is probing the scene. Fire crews managed to contain the blaze to the living room and stop it spreading to neighbouring properties.
A police spokesperson said: "Police attended following a report of a fire in a flat, where officers assisted in removing the 62-year-old occupant from the address. He is now being treated for smoke inhalation.
"Two police officers were also taken to hospital as a precautionary measure after suffering some smoke inhalation.
"A full investigation is now under way into the circumstances surrounding the fire."
Meanwhile, two pensioners had to be treated for smoke inhalation following two separate fires across the Lothians yesterday.
In Portobello, a 75-year-old woman was treated at the scene following a fire in a wastepaper basket at her flat in Rosefield Avenue. A smoke alarm alerted firefighters to the blaze just after 11am yesterday.
A spokeswoman for Lothian and Borders Fire and Rescue said: "When we arrived there was a small fire in a wastepaper basket in the flat. A 75-year-old female was treated for smoke inhalation. She was checked over and wasn't taken to hospital."
In Dunbar, firefighters extinguished a blaze in a kitchen in Lochend Road at around 6.30pm where a 72-year-old man was also treated at the scene after breathing in fumes. Crews from Dunbar and East Linton used two breathing apparatus and a hose reel to snuff out the fire.