Rescuers found a liferaft and a flare was seen by a helicopter crewman. The New Zealand Defence Force King Air provided air support and tracked the liferaft until a Coastguard vessel arrived.
The two uninjured survivors were rescued from the liferaft.
The statement said it was believed their 29ft vessel had sunk and the people on the boat were accounted for.
A Coastguard New Zealand spokeswoman told the Bay of Plenty Times the survivors were a brother and sister.
They had set out on the trip to Mayor Island when they noticed the boat quickly sinking.
As they deployed their inflatable dinghy, they activated their EPIRB beacon.
"As the Mayday call was being sent out by RCCNZ, volunteers from Auckland Coastguard, who had just picked up their new rescue vessel Trillian Trust Rescue from the boatyard, were on their maiden voyage to deliver it back to Auckland," the spokeswoman said.
"Upon hearing the mayday call, they quickly made their way to the area of operation as guided by RCCNZ and the rescue helicopters in the area, rescuing the two people at 2.47pm."
Rescue helicopter pilot Liam Brettkelly said the two people aboard the Bayliner launch did all the right things.
"When their boat began sinking, they jumped into the inflatable liferaft, let off an emergency beacon and also a smoke flare to alert rescuers to where they were," he said.
Brettkelly said the siblings were located about 2.10 pm about 9 nautical miles off Mayor Island and their boat was believed to have sunk about 7.5 miles from the island.
He praised the two quick-thinking boaties as there was quite a strong offshore breeze blowing at the time.
Brettkelly said a Westpac Rescue Helicopter from Auckland also attended the water rescue but was not required in the end.
