Christopher Abraham, 26, and his brother, Robert Abraham, 20, had left a funeral wake to "exact some retribution" on David Linning, 65, and punched and kicked him, and then slashed his face as an intended permanent reminder of what he had done.
However, Mr Linning, who was innocent of causing the facial injuries which the mother had suffered, died as a result of the beating. His body lay undiscovered in his home for two days.
The brothers, whose father, Robert "Mr Abie" Abraham, was a popular presenter on Radio Clyde in the 1980s, were led to the cells to angry shouts from relatives of their victim.
Mr Linning's son, Billy Linning, 37, who serves with the Royal Logistics Corps, said: "We are very happy with the sentence, and relieved it is all over.
"It has been absolutely horrific … everybody is totally devastated and will be for many years to come."
Mr Linning had been a well-known figure in East Kilbride, Lanarkshire, where he refereed amateur football matches for 30 years and was a volunteer with Alcoholics Anonymous.
He had tried to help the Abraham brothers, both of whom were heavy drinkers.
Billy Linning said: "He was so helpful, he was trying to help the two guys who killed him get off the drink.
"He couldn't walk two steps without stopping and talking to someone – usually about football. His name will live on."
The brothers admitted the culpable homicide of Mr Linning on 10 December last year at his home in Vancouver Drive, East Kilbride.
Mr Linning had been in a year-long relationship with their mother, Jennifer Abraham, but ordered her to leave his house because he could no longer cope with her drinking.
She tripped and fell, and gave herself a black eye. She continued drinking and sent text messages to her estranged husband, saying she had been put out the house and had a sore face.
The brothers were informed while in a "fairly heavy drinking session" at a wake, and believed Mr Linning had assaulted their mother.
"In a sober environment, this was a tragedy which would never have happened, a tragedy both for the family of Mr Linning and for these brothers," Ian Duguid, QC, defence counsel for Robert Abraham, told the High Court in Edinburgh.
"They went to exact some retribution on Mr Linning for an attack of which he was entirely innocent, with some terrible consequences. (Robert Abraham] slashed his face to give him a scar which would require some kind of explanation."
Tommy Ross, counsel for Christopher Abraham, said the lives of the parents and sons had been blighted by drink, and the accused intended to take whatever help was available in prison to tackle his problem.
Lady Stacey told the pair: "What you did that day was wicked.
"You went to the home of a man in his sixties when you were both fuelled by drink and you proceeded to attack him … two young men attacking one old man. The cause of death was blunt force trauma to the head and neck. You used a knife on his face, but that did not cause his death."
Lady Stacey said the sentence would have been 15 years each, but they were entitled to a discount for pleading guilty.