Despite being riddled with arthritis and having just undergone a hip replacement operation, John Tennant, 61, climbed a ladder to reach the man who was hanging out of a window screaming for help.
Moments after helping him to safety, the flat in Craigentinny exploded in a fireball, sending a 3ft shard of glass shooting across where the man had been trapped.
Fire chiefs today praised Mr Tennant's bravery and quick thinking.
Remarkably, it is the second time Mr Tennant has saved a neighbour's life, having earned a meritorious award from the fire service when he rescued a woman stuck in her burning Craigmillar flat in the 1970s.
Modest Mr Tennant, who needs a stick to help him walk and will have his other hip replaced within months, today told how he did not have any time to think when the blaze broke out in the Loganlea Loan block on Saturday morning.
He said: "It was about 6:30am and I was awake watching TV in bed because the pain sometimes means I find it hard to sleep. I heard a bang and then saw glass falling all over the garden. I got myself out of bed and saw Graham hanging from the window ledge, screaming 'Help me, I'm on fire, I'm burning'. He was totally black with smoke and his feet were bleeding. I was in absolute shock and wasn't sure what to do, then my wife Gwen reminded me about the ladder in the shed. I grabbed the ladder and got it against the wall.
"I forced myself up and grabbed Graham, then pulled him to the ground. About three seconds later there was a huge boom and the room exploded."
Mr Tennant said he believed the 3ft shard, which shot over the window ledge and landed in a bush, would have struck his neighbour if he had not made it down before the explosion.
"One of the firewomen who came said I was 'quite a man' but I think it's what anybody would have done in the circumstances. I didn't feel any pain at the time because I was running on adrenaline, but I'm suffering for it now. I'm feeling very sore. Graham went to the ERI for a check-up and he suffered some burns, but he is now staying with his mother and stepfather."
He added that he was very keen to find a mystery man who held the ladder for him during the rescue and then "walked off into the night".
He said: "It's important that I don't get all the credit because this guy was just as responsible for getting him down. I'd like to hear from him, whoever he is."
Mr Tennant said his previous rescue mission was in the early 1970s when he had pulled a woman from her third-floor Craigmillar flat after coming across the fire on his walk back from the pub.
Today a Lothian and Borders Fire and Rescue service spokeswoman praised Mr Tennant for his bravery.
She said: "Mr Tennant acted with great presence of mind to rescue his neighbour and there is no doubt his brave actions prevented a more serious outcome for the occupier.
"Whilst it is important that people do not put themselves at undue risk to rescue another person, sometimes quick action is necessary and obviously in this case Mr Tennant felt he could intervene and help."