During a hearing held at Sheffield Crown Court on Friday, Callum Shepherd, 20, was jailed for 10 months for dangerous driving, driving without a license and driving without insurance.
The court heard how the chase began after a patrolling police officer discovered that Shepherd's vehicle had cloned plates and indicated that he should pull over.
"The defendant travelled at speeds of 50mph in a 30 zone through a residential area, he drove straight across a roundabout without slowing down, he overtook a vehicle when it wasn't safe to do so and drove through a red light," Kate Spence, prosecuting, told the court.
"The defendant fled the scene, followed by the patrolling police officer and other officers who had arrived. In the back of the vehicle was the defendant's 18-month-old son."
Shepherd was caught a short time later, when he was taken to hospital for the injuries he suffered. His son was not injured in the collision, the court heard.
He pleaded guilty to the string of driving offences relating to the chase, which took place on November 18 last year, at an earlier hearing.
Kevin Jones, defending, told the court that Shepherd, of Browning Road, Herringthorpe was on the way to pick up medication for his seriously ill mother who has since died.
He said that when he fled the scene he ran straight to his mother's house, and arranged for a family member to go and pick his son up from the crashed vehicle.
He said: "He shouldn't have done it, he should have made other arrangements for that medication. When he realised those blue lights were for him, he drove off. And it was a particularly bad piece of driving."
Passing sentence, Recorder Simon Eckersley, told Shepherd: "I've described your driving as monstrous - and that's what it was.
"This was a very bad piece of driving. You crashed, not only damaging the police vehicle - that was bad enough, but what's worse is the fact that your 18-month-old son was in the back of the vehicle."
Shepherd was also disqualified from driving for 17-months, after which time he will be required to take an extended driving test.