Tomasz Raszkiewicz "forcibly lunged" at Lucasz Gal's mother as she held him in her arms, causing the baby to fracture his skull on a door.
Lucasz' "catastrophic" injuries mean he will have "no quality of life", Preston Crown Court heard.
Raszkiewicz, 33, admitted wounding or inflicting GBH with intent and was jailed for three years and two months.
The court heard Raszkiewicz was on the run from Polish authorities at the time of the attack on 22 November.
His name had not been included on Lucasz's birth certificate as part of his efforts to evade capture.
The court heard Raszkiewicz did not go to hospital with his son but left the couple's flat in Blackpool before his arrest three days later.
Sentencing, Judge Heather Lloyd told him: "You then lied and said this was a terrible accident. That was cowardly behaviour."
The court heard Lucasz's mother Jadwiga Gal gave the police five accounts as to how her son sustained his injuries, and it was the testimony of the boy's uncle which brought the case to court.
Judge Lloyd told Raszkiewicz his actions had resulted in "catastrophic, life-changing injuries".
"Such was the severity... a piece of his skull was embedded in his brain.
"He only survived as a result of the skill of the surgeons," she said.
The judge also criticised the boy's mother for choosing to protect Raszkiewicz rather than her baby boy.
"Lucasz will never life a normal life... and be dependent on others for the rest of his life," she said.
Raszkiewicz will be deported upon his release from prison, the court heard.
Det Sgt Chris Williams of Lancashire Police said Raszkiewicz had shown "no remorse" or "regard for the safety and welfare of this defenceless baby, who should have been safe in the arms of his mother".

The country has now seen two consecutive quarters of declining growth, the usual definition of recession.
Its vital oil industry has been hit by weaker global prices, according to the Nigerian Bureau of Statistics (NBS).
But the government says there has been strong growth in other sectors.
Crude oil sales account for 70% of government income.
The price of oil has fallen from highs of about $112 a barrel in 2014 to below $50 at the moment.
Outside the oil industry, the figures show the fall in the Nigerian currency, the naira, has hurt the economy. It was allowed to float freely in June to help kick-start the economy, but critics argued it should have been done earlier.
The government, however, has found some positive news in the figures.
"There was growth in the agricultural and solid minerals sectors... the areas in which the federal government has placed particular priority," said presidential economic adviser Adeyemi Dipeolu.
Nigeria, which vies with South Africa for the mantle of Africa's biggest economy, is also battling an inflation rate at an 11-year high of 17.1% in July.
"A lot of Nigeria's current predicament could have been avoided," said Kevin Daly from Aberdeen Asset Management.
"The country is so reliant on oil precisely because its leaders haven't diversified the economy.
"More recently, they have tried, and failed, to prop up the naira, which has had a ruinous effect on the country's foreign exchange reserves and any reputation it might have had of being fiscally responsible."
This economic recession comes as no surprise to millions of Nigerians. Many say they've never known it so tough.
The slump in global oil prices has hit Nigeria hard. The government depends on oil sales for about 70% of its revenues.
But critics say government policies made a bad situation even worse. The decision to delay devaluing Nigeria's currency meant many businesses struggled to get foreign currency to pay for imports, which had a cooling effect on the entire economy.
Following enormous pressure, the government changed tack this summer, allowing the naira to float.
That's led to a spike in inflation, but the hope is that it will attract foreign investors. The government also says the country needs to import less: it wants to see more products made in Nigeria.
A father whose drunken attack left his newborn son with severe brain damage has been jailed.
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Nigeria has slipped into recession, with the latest growth figures showing the economy contracted 2.06% between April and June.