The Westpac Rescue Helicopter winched two people aboard and a police helicopter found the third person in the water.
A police crew member jumped into the sea with a flotation device to rescue him and both were then picked up by a police launch.
Two of those rescued were taken to Auckland Hospital.
Inspector Shawn Rutene said the 13-year-old boy was believed to have separated from his three other family members some time during the night.
"Indications tell us so far they were all huddled together on the boat, it was dark, it was pretty rough and at some point during the night or early morning the parties have separated,'' Mr Rutene said.
The boat capsized halfway between the Coromandel and Waiheke Island, which Mr Rutene said was "a place that you really don't want to be in the water''.
Coastguard operations manager Ray Burge said the capsized vessel was "a small boat ... for the conditions and the number of people on board''.
"They certainly should have checked the marine weather before they went out. A vessel that size with four people, probably not the best,'' he said.
None of the four members of a Papakura family whose runabout capsized in the Hauraki Gulf were wearing lifejackets, despite there being more than enough for everyone.
Coastguard spokeswoman Georgie Smith stressed the importance of not just taking lifejackets on a boat trip but wearing them.
"The four people involved in today's incident weren't wearing lifejackets, yet there were five lifejackets in the boat.''
She said the survival rate for people wearing life jackets was ten-fold that of people who did not.
"If they were all wearing lifejackets the chances of finding them are just huge, as are their lack of hypothermia, because they can also keep you warm.''
Ms Smith said safety messages were stressed throughout the year but many people still did not take them seriously.
"We can only do so much - our volunteers have been out there dedicating their time, risking themselves today to save others, but people need to look after themselves.''
Water Safety chief executive Matt Claridge said there seemed to be a particular resistance to wearing lifejackets from Pasifika people.
"In the last 12 months it has been a rising issue''.
Mr Claridge said it was practically impossible to put on a lifejacket in the water.
"As an incident unfolds on a boat, it's nigh on impossible to get everybody in a lifejacket in time - hence why the most obvious and logical thing to do is to wear a lifejacket when you're in a boat in case you fall in the water.''
He said it was especially important for children to wear safety gear.
Maritime New Zealand deputy director Lindsay Sturt said it appeared the group also had no means of communication.
"We sympathise with the family in what is an extremely difficult time, and we are hoping for a positive outcome to the search, but it appears this situation could so easily have been avoided,'' Mr Sturt said.
"These men were not wearing lifejackets and it appears they had no means of raising the alarm when they got into trouble - that means they spent 12 hours in the water even before a search began, in the middle of the night.
"We hear of rescues every week from around the country and almost, without exception, when people take simple steps to prepare for boating trips, the outcomes are positive.''
Police also stressed the importance of being safe on the water.
A police spokesman said skippers needed to urge everyone on board their vessel to wear lifejackets.
"Make sure that your boat is equipped with a marine radio, a cellphone and flares.
"Importantly, check the marine forecast before you go out and if the conditions don't look good then don't go out.''
