The aircraft reached the ship's last known location about 6am and found the life raft about 15 minutes later.
Helicopter crewman Phil Dwyer said they found an oil slick where the boat had sunk and began to search northwest from there, in the direction of the currents.
They found the life raft about 2km away and winched down a rescuer from a height of about 15m.
"We left him on the wire, got him in the water and he swam over and did three winches, and got them all to safety,'' Mr Dwyer told APNZ.
It was a textbook rescue despite a couple of big 4m swells in the middle of the operation, he said.
"At that stage it made things a little bit more tricky. It was rough out there, and it's hard winching down and putting someone onto a life raft because you can't come down too low, because the wash of the helicopter can blow it around a bit.''
Mr Dwyer said the three men in the raft were cold and wet, but uninjured.
"When we got them into the aircraft I think they were pretty happy.
"It's funny, the first guy we brought in, the excitement on his face - I think it was more that he knew he was going to get a ride on a helicopter, rather than the fact that he'd been saved.''
The men were taken to the Taranaki Base Hospital for medical assessment.
Mr Dwyer said the fishing crew had mostly done everything right, but did not appear to have a personal locater beacon on the life raft.
"If the first signal had not gone off and given that location, it would have made things a little bit more difficult.
"I think we had about probably maybe 40 minutes' fuel endurance left, so we couldn't have stayed out there for much longer.''
The Spirit of Resolution was about 2km away from the life raft by about 6.30am and remained on scene while the men were winched to safety, in case assistance was required.
Mr Dwyer said the Rescue Coordination Centre and local authorities had done an excellent job of coordinating the rescue.
The ship's owner, who stopped by the helicopter hangar this morning, was not too worried about his vessel but was more concerned about his crew.