The fleeing driver continued at high speed on the motorway until the car was spiked at Mt Wellington.
The car was then followed as it started to lose tyre pressure. But police stopped the chase after the driver turned off the motorway at Highbrook before re-entering the motorway again turning south in a northbound lane at Highbrook.
"It continued south for a short distance, collided with the concrete barrier, and the three occupants then ran from the vehicle, leaving it across two lanes of the motorway," police said.
Shortly afterwards a northbound vehicle smashed into the abandoned vehicle. The driver was checked by ambulance staff but escaped with bruising.
The fleeing offenders in the stolen vehicle are yet to be found.
The trio were thought to be male youths, police said.
The stolen vehicle would undergo forensic examination in the coming days for clues in identifying them.