Areas covered by watches due to what the weather service's Las Vegas office calls "abundant tropical moisture from Hurricane Rosa" include southern Nevada, southeastern California, southwestern and central Utah and the western two-thirds of Arizona.
Hurricane Rosa rapidly lost strength off the coast of Mexico on Saturday as it moved towards Baja California, the US National Hurricane Center said.
The National Weather Service says surf from 6 to 10 feet (1.8 to 3 meters) is possible on Los Angeles and Ventura County beaches as early as Saturday night or Sunday.
It's rare for a hurricane or tropical storm to impact the southwestern USA, but CNN meteorologist Gene Norman says, "These events have begun to increase in recent years".
Heavy rainfall is expected across the Baja peninsula as well as the southwestern United States, with the potential for life-threatening desert flash flooding and mountain landslides, the hurricane center said.
Sergio had winds of 50 mph (85 kph) early Sunday and it was centered about 485 miles (780 kilometers) south of Manzanillo, Mexico.
Up to 4 inches could fall in Flagstaff, Payson and Prescott through Wednesday. Harvey, which made landfall north of Corpus Christi late Friday evening, is expected to dump upwards to 40 inches of rain in Texas over the next couple of days.