Nelson Surf Lifesaving Club president Marcus Gardner led the rescue, with help from fellow volunteer Aaron Lyttle.
He told the New Zealand Herald this morning water was lapping at the tyres of the stranded group's 4WD vehicle when they arrived.
"Anyone in the river is in danger. Last year we had a guy swept away in that river and drowned ... [last night] they were completely stuck and the water level was rising ... and it was pretty stormy, gale force weather."
The group appeared to be 4WD enthusiasts, based on their vehicle, and he understood they went to the stopbank road as part of a group of 4WD vehicles.
Mr Gardner and Mr Lyttle reached the stranded group after motoring about 500 metres upstream from a road where police, firefighters and ambulance officers were waiting.
The farmer who owned the land - and who will today be repairing cut fences - told them the best route to take.
The group were stranded on what looked like an island, but was actually a hump in the road surrounded by rising water, Mr Gardner said.
They were pleased to see their rescuers.
"[The mum] was just keen to get out of there. She was worried about how cold and wet it would be to get out of there, but we bundled them up ... with thermal blankets ... and put them in the boat."
The adults were given lifejackets, but the baby was too small for the baby-sized lifejacket on board, Mr Gardner said.
So her mum tucked her in between her own body and lifejacket during the five minute return journey, he said.
"The baby was inside her. She was happily snuggled into mum, she barely even squawked, just a few squeaks and that was it."