The car exited the motorway at Ramarama before getting back onto the motorway heading north bound, this time on the right side of the motorway.
The driver then made a U-turn and crashed into a police vehicle.
The driver turned back the correct way but crashed into a truck near the Papakura off-ramp.
Police say a member of the public helped an officer in apprehend the driver and two passengers of the vehicle. The entire incident lasted about 28 minutes.
An 18-year-old female, 15-year-old male and 12-year-old female are all in police custody.
Glossop said: "this type of behaviour has to stop as it is only a matter of time before someone is seriously injured or killed.
"We are now limited in what we can say as this matter will be going before the courts but we want to express our deep concern by this type of offending. Hundreds of members of the public going about their daily business were put in immense danger and it is simply unacceptable."
Earlier, a police spokesperson said the vehicle drove in the wrong direction on the Southern Motorway.
The vehicle appears to have crashed into a truck at the Papakura interchange, partially blocking the north-bound lanes.
There were no reported injuries and three people are now in custody.
NZTA confirmed both northbound lanes were temporarily blocked to enable vehicle recovery but had since reopened.
There is congestion from Drury to Papakura. Motorists should expect delays.
* Police request that anyone whose vehicles might have been damaged in the incident contact Sergeant Nick Ewen on 09 261 1300.
