The 19-year-old from San Jose was playing with friends in the river. He was able to grab onto a rock and hold on until help arrived.
Rescuers tried to reach him by boat and by climbing out onto the rocks.
In the end, they decided it was best to hoist him to safety using the Sheriff Department's helicopter.
The teen was taken to a waiting ambulance, but refused medical aid.
"Basically," says Sgt. Mark Baldwin of the Kern County Sheriff's Dept., "(he) was just not strong enough to assist at all. … We felt that, if he was knocked free (of the rock), that he was going to end up going downstream. That would have just made the problem even worse."
Click on the video below to see the rescue as CBS News Correspondent Jeff Glor tells the story: