One of the rescuers, David Phung, jumped into the brown water and pulled the woman to safety before diving back in to rescue her dog.
Alex Cobb, one of the motorists stranded for a day, said she had been on her way to a bridal shower with food, which she used to feed those who were stuck.
The driver of a grocery truck also shared produce with the marooned motorists.
In one suburb of Baton Rouge entire shopping centres were inundated with water. In car parks only the tops of cars peeked above the water.
Shanita Angrum, 32, described how a police officer carried her six-year-old daughter to safety after they became trapped in their home.
She said: "Snakes were everywhere. The whole time I was just praying for God to make sure me and my family were OK."
Lyn Gibson, another resident, said she got to safety by hacking a hole in the roof of her house using a saw, screwdriver, and her feet.
She said: "I just kept picking and hitting and prying until I could get a hole big enough."
Eventually, she made it out along with her dogs and was rescued by National Guard soldiers on a boat.