Police hope someone saw their dramatic escape, or knows who the men are, and will come forward with information.
The victims, including the heavily pregnant woman, were threatened with a shotgun and robbed of cash, cellphones, and electronic items after the three masked men forced their way into the family's home.
No shots were fired and they weren't injured but have been left deeply traumatised.
Detective Sergeant Andrew Wong, of North Shore CIB, said there were two patrol cars close by when the 111 call was made.
"It was a very, very traumatic experience but they managed to get that phone call to us."
He told the Herald the robbers fled in the stolen car before it was spiked and crashed into bush near Kaipatiki creek.
"They've run off up into the bush and run into Manuka Rd and Heathglen Pl.
"So we are very interested to know if anyone saw them there.
"They would have been very wet because they ran through a creek."
Mr Wong appealed for any sightings of the three men running or anyone who may have had their car broken into or stolen.
Police believed they were not from the area and so would have needed transport to get away.
"They had to find a way to get out and the usual way is to find a car and get out that way."
Mr Wong said someone close to the robbers would also know something had gone on.
"Someone will know if their partner is getting home in the early hours saturated ...
"Someone will have received a phone call [to come and get them], so they will know."
The robbery was a low act, he said, particularly because a heavily pregnant woman had been threatened with a gun.
"They're certainly not remorseful about what they were doing."
The victims, an Asian family, were recovering from their ordeal and didn't want to talk.
Mr Wong would not discuss what happened inside the house but confirmed that the trio forced their way in.
He said there was nothing to indicate yesterday's robbery was related to a similar one in Pinehill last month.
But the possibility had not been ruled out.
The 37-year-old man arrested yesterday appeared in the North Shore District Court charged with aggravated robbery.
CAN YOU HELP?
Three men were seen running through Manuka Rd and Heathglen Pl, Glenfield, during the early hours of yesterday morning.
If you saw them, or if your car was broken into or is missing, phone North Shore police on 09 477 5000 or contact Crimestoppers anonymously on 0800 555 111.
