Tony Bartlett, of Axminster, Devon, faces a minimum term of 18 years behind bars after attacking Atticus Bartlett on 16 July 2022 in a "sudden fit of anger".
The 39-year-old and his then-partner Evelyn Ballentyne, Atticus's mother, had gone to a pub and comedy club that evening, Bristol Crown Court previously heard.
Bartlett drank eight-and-a-half pints of lager over the course of the evening before returning home with Ms Ballentyne, and was left alone to feed Atticus in the living room, while she went upstairs to change around 11pm.
He then violently shook Atticus, it was alleged, causing severe internal injuries to the baby's brain and spinal cord.
Atticus' brain damage was so severe that he did not regain consciousness or manage to breathe for himself, and he died at Bristol Royal Hospital for Children just before midnight on 23 July 2022.