"I was running in ... I ran into the room and then she was born," Ms Te Kanawa said.
Ms Te Kanawa said her daughter was born within minutes at 3.10pm on Friday - 10 days past her due date - and weighed 3.9kg (8lb 7oz).
She was delivered by staff doctors Anne Dibley and Des Epp and a nurse.
"They were amazing. I don't know what we would've done without them.
"We barely made it."
Ms Te Kanawa said her daughter's birth was unexpected because her contractions, when she left for the hospital, were still about 10 minutes apart.
"I thought I was nowhere near ready."
The birth was so unexpected Ms Te Kanawa's mum and midwife weren't even there as they had gone ahead of them to the hospital.
By the time the couple rang them the baby had arrived.
Ms Te Kanawa said she was home by 4pm. She said getting the baby out of the surgery took longer than the labour and delivery because the staff were excited about what had happened and wanted a cuddle with her.
"The nurses and doctors all wanted a cuddle ... the doctors were high-fiving each other."
Dr Dibley said the surgery had been unusually quiet on Friday and when Mariana walked in in the "later stages of her labour" it caused a bit of excitement.
She said both she and Dr Epp had "delivered many babies in the past" but this baby was the first one they had delivered at the doctor's surgery.
Dr Dibley said everyone at Owhata Surgery helped with the delivery. Reception staff helped Ms Te Kanawa into the room and the nurses helped with the equipment.
"It was a team effort. It was a pleasure to be of help."
Mr Gage also rang his mother Neldarene Gage and told her about the baby being born but she didn't believe him and hung up because she had left the couple half an hour earlier.
"I thought he was joking because he's a joker. From now on I'll believe him," Mrs Gage said.
The couple have a few name options for their daughter but they haven't settled on one yet. However, she said the baby wouldn't be called Owhata.
The newborn is a younger sister for their 3-year-old son Manaaki. When The Daily Post asked Ms Te Kanawa if the couple would be having more children she said it "depends how much trouble she is".