A 25ft (7.5m) vessel sent a mayday call while travelling two miles north of the Isle of Wight at 13:20 BST on Good Friday.
The boat had suffered engine failure and was taking on water, a spokesman for the Gosport and Fareham Inshore Rescue Service said.
The crew pumped the water from the boat and towed the family back to safety.
A baby girl and her parents have been rescued from a sinking boat in the Solent.