The incident occurred along Road Runner Road, according to tweets posted by the Los Angeles County Sheriff's Department's Santa Clarita Valley station.
The driver in the overturned vehicle was rescued by nearby good Samaritans and was safe, according to the tweets.
A video taken by witness Krystina Reyes showed her uncle on top of the vehicle as the rushing water brought mud and debris flowing toward the car.
"We all just dumped out the van. My uncle was like, 'Call 911,'" Reyes said.
She said he used a rock from the river to break open the window to pull the driver out. Margarito Martinez, the driver, was trying to cross the road when his vehicle was flipped by the strong current.
Martinez is a neighborhood gardener and one of his clients bought him a replacement SUV so that his business will not go under.
"He's worth it. He's a good person, and I'll get it back. God will give it back to me," Dennis Neice said.
Reyes said after the rescue she hugged her uncle thinking that could have been them.
Neighbors said they were also raising money to get Martinez a new phone and other tools for his business.
Road Runner Road was shut down due to hazardous conditions, sheriff's officials said.
The storm brought light to moderate rain across most of the Southland on Thursday. The wet weather was expected to last until early Friday morning.