Marc McKinlay, 38, assaulted Donald Maguire, 58, at Haymarket station on February 20, 2020.
The High Court in Edinburgh heard McKinlay pushed Mr Maguire on his body which caused him to fall and hit his head off the ground.
McKinlay then kicked Mr Maguire’s son Brian on the body before striking him on the head with a bag containing cans of alcohol.
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Brian’s father later died in hospital and McKinlay was arrested after getting on a train.
McKinlay, of Cowdenbeath, Fife, was found guilty of culpable homicide at the end of a four day trial.
He had pleaded guilty to assaulting Brian to his “severe injury” at the start of proceedings on Friday.
Judge Fiona Tait remanded McKinlay in custody ahead of his sentencing hearing next month.
Mr Maguire died from his injuries at the Western General Hospital in Edinburgh on March 4, 2020.
During proceedings, the court heard that Mr Maguire and his son had been enjoying a night out in Edinburgh and had both gone to Haymarket station to catch a train back home.
Eyewitnesses told the court that the Maguires came into contact with McKinlay, who was also there to catch a train. One witness said she thought McKinlay was drunk.
Architect Hugo Target, 35, told prosecutor David McLean that he was commuting home to Fife when he witnessed the incident.
He said he saw Mr Maguire fall backwards and that he landed on his back and “bashed his head”. He then said he saw Mr McKinlay strike Brian.
Mr Target added: “Following that, I saw the man carrying the plastic bag swing his arm with the plastic bag and it hit the son on the face.
“There was some punches after that. I helped to separate them. I said something along the lines of ‘that’s enough’; and I pulled the man with the plastic bag off the son.
“He then went downstairs and got on a train - it was the same train that I got on. Two officers then came on and took him off it.”
Personal assistant Katie McCulloch, 40, was returning home from a work’s night out when she came face to face with McKinlay on the train.
She had earlier witnessed the incident involving Mr Maguire and his son.
She told Mr McLean: “I remember feeling quite frightened. He was carrying some beers. I thought he was drunk. He was swearing. He was saying ‘oh for f**k’s sake, he’s a f*****g a******e’.
“I backed away as he swayed onto the platform.”
Ms McCulloch also told the court about McKinlay’s attitude when police officers told him to get off the train. She said she sat close by as he spoke to police officers.
She added: “I remember him pointing back towards his beers. He seemed to be more concerned about his beers than what happening on the stairs.”
Travel agency worker Connie Dalrymple, 29, told Mr McLean that she saw a “bit of a fight”.
She said she and her partner gave Mr Maguire CPR and she phoned 999.
McKinlay did not give evidence in his defence.
He will be sentenced on August 3.