Police turned on lights and sirens but it failed to stop.
Police followed the vehicle for about 30 seconds before it crashed, flipping on its roof as it struck a power pole and parked car at the Ladies Mile and Marua Rd intersection.
The Serious Crash Unit was now investigating.
St John Ambulance said one person was in a serious condition and the other had moderate injuries.
Power was out to nearby residents for about an hour.
A witness said it appeared the car lost control hitting a power pole and rolling into a parked vehicle.
Power lines brought down in the crash were lying across the middle of the road.
