A white Holden Commodore was spotted by police shortly after on Marion Road in Sturt, before it was allegedly rammed into the rear of a police vehicle.
Police pursued the car along Marion Road before deploying road spikes that punctured one tyre.
Three kilometres later the car crashed into another police car in Plympton Park, where the men were arrested.
No one was injured.
Both men have been charged with aggravated robbery, while the 33-year-old has also been charged with endangering life and engaging in a police pursuit.
They have been refused bail and will appear in Adelaide Magistrates Court on Monday.