The group became stranded "a couple hundred yards from shore" near Looe, Cornwall, with the boat "filling with water", the RNLI said.
Two lifeboats were launched after several people reported the stricken vessel at about 16:30 BST on Sunday.
All the people onboard were taken to shore and the submerged boat was towed in to harbour.
The RNLI said by the time the lifeboat reached the small speedboat waves were breaking over the vessel and flooding it at Plaidy, East Looe.
Dave Haines, Looe's lifeboats operations manager, said: "Those rescued were lucky they were spotted by someone ashore.
"If it had been a bit later, the outcome might have been different. Although they were all wearing lifejackets they were a couple hundred yards from shore, over the rocks with a strong swell'.
He said several lifeboat crew and people on the shore helped the local group who were "wet through and cold" but otherwise safe and well.
Five people and a baby were rescued from a sinking speedboat in a "strong swell".