A police spokeswoman said the males, two aged 18 and one 15, were arrested in Waihola following the attempted carjacking in Gowland St, North Dunedin, at 1.50pm today.
Police were alerted by a member of the public who managed to provide the registration plate details for a car the teens were travelling in.
After making inquiries, officers found it in Corstorphine later in the afternoon and followed it to Waihola in South Otago.
Police deployed road spikes, which brought the car to a stop, before the teens fled on foot.
Dog units were brought in to track the trio and found them in three locations about 90 minutes later.
The teens were taken into custody and face a range of charges, the spokeswoman said.