Two men, both aged 23, were arrested when the car was abandoned in Suffolk Court around 6.15 pm after police deployed a stinger device.
A third person, who was a passenger in the grey-coloured Citroen C5, escaped from the scene on foot.
The officers were hurt when the Citroen reversed into their vehicle. Neither need hospital treatment.
The car had been reported as stolen from a filling station on the Stewartstown Road earlier on Tuesday.
The driver was arrested when the car was abandoned, and a passenger was detained a short time later.
Police are still looking for the third individual and have appealed for anyone with information to contact them on 0845 600 8000.