A police spokesperson said they had an increased presence in the wider Dunedin area as a group of gang members travelled in procession from Balclutha to Corstorphine.
The three people arrested were charged with failing to stop for police, dangerous driving, and obstruction.
Two vehicles were also impounded, the spokesperson said.
"There is a zero tolerance for dangerous driving behaviours, and those that decide to act poorly should expect action to be taken and follow-up enforcement."