The suspects matched descriptions from several vehicle-related offences, the spokesman said.
Christchurch Police received reports of dangerous driving involving the stolen vehicle on Sunday.
After the vehicle fled from police in Christchurch, road spikes were used to stop the driver.
The pair were taken into custody.
The youths face multiple charges, including petrol thefts, dangerous driving and failing to stop for police.
Senior Sergeant Mel Robertson said the pair were “extremely fortunate” they did not injure themselves or other road users.
Police continue to investigate and urge anyone with further information to come forward.