"It was a bucket list trip," Andrew Bindon said.
"My stepmother is Mexican and they bought the boat just over a year ago. They were supposed to do the trip this time last year but they didn't have all the right stuff - life rafts and that sort of thing - so they postponed it until now.
"They were on the last leg going between Rarotonga and Tonga when this happened."
Mr Vereker-Bindon and Mr Boyd were asleep when the fire started.
"Victor smelled smoke in the cabin and so he went and opened the engine hatch to see the engine bay was on fire," Andrew Bindon said.
"Smoke started billowing into the cabin. He woke my father and Michael and they had a matter of seconds to grab the life jackets, set off the emergency beacon and jump off the boat. The smoke was toxic, they had to go.
"All my father had with him was the life jacket and the underwear he was wearing."
The three men then had to swim around to the back of the burning yacht and detach the life raft.
They managed to cut the rope that attached it to the yacht and climbed in to wait for help.
It is thought they floated for about four hours before they were found.
The emergency beacon was registered in Germany and once the alert was received by the Marine Rescue Coordination Centre in Bremen the Rescue Coordination Centre New Zealand was contacted.
RCCNZ identified ships nearby and the Liberian-flagged container ship MV Cap Capricorn was the closest at just over 38km away and was requested to divert and provide assistance.
"When they arrived on scene they saw the glow from the burning yacht and blasted their whistle to attract the attention of any survivors," said RCCNZ search and rescue mission coordinator Dave Wilson.
"After around 30 minutes of searching they saw a distress flare fired in response. The life raft was located and the ship manoeuvred alongside. The three sailors were able to board the ship via the pilot ladder."
First aid was provided on board but none of the men were seriously injured.
They were given clothes and will remain on the MV Cap Capricorn, which is due to arrive in New Zealand on Saturday.
"It was an excellent piece of seamanship to bring a 228m ship alongside a liferaft in these condition. We'd like to express our appreciation to the Master and the crew of the MV Cap Capricorn for their efforts," said Mr Wilson.
"The crew of the yacht were also well prepared - they had a registered EPIRB, which enabled them to be identified quickly, their liferaft was in good condition, and they had a distress flare to respond when the ship arrived. In the circumstances it was an excellent result."
Another of Mr Vereker-Bindon's children Matthew had been tracking the SV Sunny Deck on its journey and was first to hear of the drama.
He called Andrew Bindon to deliver the news at 6am.
"The first thing he said was that they were all safe," said Andrew Bindon.
"I knew that everything was going to be ok. It was a pretty big shock though because my dad's pretty cautious when it comes to these sorts of things.
Matthew Vereker-Bindon said he had spoken to his father a few times today via the container ship's phone.
He said they were "all ok".
He sent the Herald a photo of the three men, taken during their voyage to New Zealand.
Mr Vereker-Bindon splits his time between Mexico and New Zealand, where he worked as a lawyer. He is now retired but according to the Ellice Tanner Hart website he still works for the firm as a consultant.
He and his wife run a student exchange programme in Acupulco, offering school exchanges between students from Mexico and New Zealand.
