It took the ship's crew six hours to notice he was missing.
Declaring an alarm and radioing a distress to the Joint Rescue Co-ordination Centre in Tahiti, the crew worked out Perevetilov had been onboard at 4am because he filled a report log at 4am, Stuff reported.
French navy aircraft joined the search from Polynesia, while France's national meteorological service assisted by calculating probable drift patterns.
Meanwhile, an exhausted Perevetilov battled to keep himself afloat through a difficult night.
With the dawn's light he noticed a black speck on the horizon and swam towards it.
"It turned out to be an old fishing buoy," Marat told Stuff.
"It was just a piece of sea rubbish."
However, it floated and Perevetilov was able to cling to it and survive.
As he bobbed in the water his hopes of being rescued were answered.
The Silver Supporter found Perevetilov close to 17 hours after he had toppled over the deck.
It had been performing a set search pattern when a passenger on board the vessel heard a faint voice to the side of the ship and he was pulled aboard, tired but alive.
British High Commissioner to New Zealand Laura Clarke, who also acts as Governor of Pitcairn Islands, told the Herald everyone was "hugely relieved" to hear of the rescue.
"We all feared for the worst, given the sheer scale of the Pacific Ocean, and its strong currents," she said.
"So the fact that the Silver Supporter found him, and he survived is just amazing: a story of survival that even Captain Bligh ... would have applauded."
Vice-Admiral William Bligh travelled 6700km in an open boat after being cast adrift while Captain of the Bounty by mutineers in 1789.
Members of the mutinous crew later became the first inhabitants of Pitcairn Island.
Perevetilov's son Marat, meanwhile, told Stuff he was amazed his dad hadn't taken the fishing buoy that saved his life onboard with him as a souvenir.
"It's funny. He said he wanted to leave it there, so it could save another person's life," he said.
