Emergency officials say all six had life-jackets on when the raft flipped after striking a bridge abutment early Sunday evening.
Five made it to shore but the sixth passenger — a woman in her 20s — clung to the craft after it became pinned against the bridge.
She was calling for help when firefighters lowered a rope to prevent her from slipping away before an aquatic rescue team rappelled down to hold her until a boat arrived.
The woman was conscious and alert when she was brought to shore and taken to hospital.
Prior to the rescue, authorities had to call off would-be civilian rescuers for fear they might fall into the river.