Police say officers noticed a suspected stolen car in Caffrey Avenue around midnight.
The vehicle collided with police car before heading off towards the Glen Road.
Minutes later the vehicle hit another police car after it reached the Whiterock Road.
A man, aged 19, and a youth, aged 16, were arrested in the area by police officers giving chase on foot with the aid of a helicopter hovering overhead.
They are being questioned at the PACE custody suite at Musgrave PSNI station on suspicion of burglary and a number of motoring offences.
Police said they had received a report shortly 10 pm last night of a car matching the description of the one used in the incident as being stolen during a creeper burglary in Bladen Drive in south Belfast.