Steven Pickering, 32, momentarily lost control and gripped, shook and threw down 11-week-old Logan.
But Bradford Crown Court heard that the father had a 'significant learning difficulty' and should never have been left alone to care for the baby.
His Honour Judge Rose said Pickering could have killed his son but decided not to send him to prison.
The verdict sparked angry scenes in court. Logan's mum, Sinead, said afterwards: "He almost killed his own son and should have been locked up.
"I feel disappointed and let down by the system that it has taken since 2010 for this to come to court. But even now Steven hasn't said how the injuries were caused."
Denise Breen-Lawton, prosecuting, told the court Pickering, who had a daughter by a previous relationship, did not work and was described as 'lazy' at home, doing little to look after Logan.
Sinead was taking a hairdressing course at Huddersfield Technical College and on January 16 left Pickering to look after Logan on his own.
At lunchtime Pickering phoned 999 and paramedics arrived. Pickering said Logan was 'floppy' and 'breathing funny' but insisted nothing had happened.
At first medics suspected meningitis but investigations subsequently found that Logan had suffered a fractured skull and bleeding on the brain.
A doctor later said Logan had been subjected to 'significant forces'. It was likely the baby had been 'held, shaken and thrown down'.
Pickering denied hurting his son but admitted to being 'a bit heavy-handed or rough' but no-one had shown him how to handle a baby.
Handing Pickering a 12-month sentence suspended for two years, Judge Rose said: "A child is precious and needs to be protected and handled gently and carefully.
"They do not always do what we want. They often make noises and messes that we don't want them to.
You did something very bad to him when he was only a few weeks old. You hurt him, you shook him and threw him down and broke his skull. It's an injury that could hurt him for a very long time. It could have killed him.
It is hoped Logan, who will be three next months, will suffer no lasting effects.
More on Parentdish: Couple who broke toddler's legs spared jail because they are 'hard working'
More:Advice And Health
Suggested For You
Get top stories and blog posts emailed to me each day. Newsletters may offer personalized content or advertisements. Learn more