Daring rescue in the middle of a historic storm dumping tons of rain on Los Angeles ... firefighters used a helicopter to save a man who jumped in a raging river to grab his dog.

The emergency situation played out Monday afternoon in the middle of the flooding L.A. River ... with LAFD crews bringing in a chopper to pull out a man who was stranded in the flowing water.

The guy was trying to bit somewhat of a hero himself ... he was attempting to save his dog, who had been swept away in the rapids during a flash flood.

As you can see, a helicopter hovered over the river and lowered a firefighter who grabbed the guy and pulled him to safety.

The poor pooch was saved too ... with the dog swimming to dry land on its own.

LAFD says both man and dog suffered minor injuries ... the guy was transported to a local hospital and the pup was taken to an animal shelter.

Firefighters are happy to report the dog is "alive and eager to reunite with his human."

As we reported ... the big storm, a Pineapple Express, is wreaking havoc in Southern California ... causing flash flooding, catastrophic landslides, and damage from debris and downed trees.

Cue Arnold Schwarzenegger ... get to the chopper!!!