The 20-year-old told police and social workers he had fallen asleep on the sofa with Oskar Jobey-Kennedy and woken to find him unresponsive.
But Kennedy, of Heysham, Lancashire, had in fact pushed his fingers into the baby's mouth to silence his screams and fatally starving him of oxygen.
Preston Crown Court heard Kennedy was jealous of his girlfriend's affections for their baby.
Oskar was taken to the Royal Lancaster Infirmary but was tragically pronounced dead shortly afterwards on October 1st 2015.
Kennedy was found guilty of murder and faces a life sentence when he comes back before a judge next week.
Oskar's mother Tia Jobey, 19, previously admitted causing or allowing the death of a child and was jailed for 30 months earlier this week.
The court heard Kennedy and Jobey had a turbulent relationship and would often row about Kennedy's cannabis use and his immaturity.
Neighbours heard them arguing loudly and could smell cannabis coming from the flat on a regular basis.
Opening the trial, prosecutor Paul Reid QC read a string of angry Facebook messages between the couple, sent in the weeks before Oskar died.
In one message Jobey said: "I don't care what you think Kane, I'm not trying to control you.
"I'm trying to make sure Oskar is happy and safe and while you are addicted to weed and violent and abusive he's not safe at all!
"You throw him around like a toy, suffocate him, stick your finger down his f*****g throat! And he's always in the middle of our arguments and fights."
At around 8.45am on October 1, Kennedy made a 999 call, telling the operator: "I fell asleep on the couch with my son last night and he's not breathing."
Police and paramedics attended the flat and found Oskar unresponsive, but still warm.
Attempts to resuscitate him were unsuccessful and the little boy was pronounced dead at at 9.44am.
Shockingly, the young couple continued their relationship following the death of Oskar on October 1 last year.
In February they learned they were expecting a second child but just two weeks later Kennedy was arrested on suspicion of murder.
He said: "I guess it felt like we had lost our purpose. Tia wanted the chance to be a mother again and I wanted to be a father again."
Speaking after the verdicts were delivered, Detective Chief Inspector Jon Holmes said: "The level of injuries inflicted on this defenceless child by Kennedy are frankly obscene.
"It is almost impossible to understand the mind-set of someone who could do this to any child, let alone their own son.
"I would like to thank the jury for their careful consideration of what must have been a hugely distressing case and I welcome the decision they have made today.
"My thoughts remain with the wider family of baby Oskar who have been through so much over the last year.
"I hope that this verdict can offer them some comfort as they try to move on with their lives."
