The car stopped and shots were then allegedly fired at police, missing officers, before the car was driven away.
The car then drove off but was spotted by another patrol car and the pursuit started again.
The woman allegedly shot at the officers from the passenger window of the car but again missed.
Police said the chase continued until the car collided with a police car on Summerland Drive.
The man got out of the car holding a sawn-off shotgun and allegedly shot at the officers, who had taken cover behind the car.
The man and woman ran off into a residential area.
A large number of officers had already been deployed to the area and cordons were put in place around the Ranui area.
The Armed Offenders Squad and Police dog units began searching the area.
Half an hour later, police arrested the woman who was trying to leave the cordoned-off area in a taxi.
A large number of officers continued the search for the man and two hours later he was found hiding under a car in a shed, on a residential property in Munroe Road.
He still had the gun when found by police and a Police dog was used to arrest him.
The man was taken to North Shore Hospital with dog bites.
Superintendent Bill Searle, District Commander, Waitemata Police said he was extremely proud of the officers involved.
"This was a very dangerous situation and it is a credit to our staff that no-one was killed or injured.
"From the time the car failed to stop at the checkpoint to the point at which the offenders crashed into our patrol car was a period of around only 4 minutes.
"In that short space of time our officers have been fired upon multiple times.
"Our staff have then searched for an armed and active gunman in the dark and have managed to locate and apprehend him.
"They have protected innocent members of the public in the most dangerous of situations.
"We all know that this could have ended very differently and I know that there will be many people who are very relieved this couple have been caught" says Superintendent Bill Searle, District Commander, Waitemata Police.
The officers involved were all uninjured.
Both the man and woman will be facing a range of serious criminal charges.
The 23-year-old woman is expected to appear in court this afternoon.
It's not known yet when the man will appear and a further media release will be made in relation to this.