Christopher Abraham, 26, and Robert Abraham, 20, were sentenced at the High Court in Edinburgh for the death of 65-year-old amateur football referee David Linning.
Father-of-six Mr Linning had started a relationship with the killers' mother, Jennifer Abraham.
The sons were at a funeral wake when they heard their mother had been injured after being told to leave Mr Linning's home.
She sent a text saying she had a "sore face", which the brothers took to mean she had been assaulted.
But Mrs Abraham had tripped and fallen outside when drunk.
The brothers went to Mr Linning's house in Vancouver Drive, East Kilbride, in December last year and punched and kicked him.
Mr Linning was found lying on the floor at his house two days later by a friend. He had a fractured nose and rib and bruising to his face.
The pair were charged with culpable homicide.