Forecasters say Rosa has already started to weaken as it curls north off Baja California.
Swells generated by the hurricane were also expected to produce life-threatening surf and rip currents off Southern California.
Rosa, with maximum sustained winds decreasing to nearly 120 miles per hour (195 kph), was now a Category 3 storm, coming down a notch on the five-step Saffir-Simpson Hurricane Wind Scale. From there, Rosa will make a clear path across Arizona and into Utah and Nevada.
At least 11 people have died in recent days in flash floods caused by heavy rain in Mexico's Pacific coast states of Michoacan and Sinaloa.
It won't be a hurricane, but the remnants of tropical storm Rosa are still on track to pummel large swaths of the state with inches of rain during the first part of the week.
The best chance for rain in Mohave County is late Sunday night into early Monday morning.
The rainfall is expected to hit Arizona late Sunday and early Monday, before the rain becomes more widespread into the middle of the week.
There is a flash flood warning in effect Monday and Tuesday for Phoenix and surrounding areas. The potentially unsafe conditions are expected to last through Monday. Some areas could get up to 6 inches.
It's then expected to move quickly northwestward as it weakens, bringing 2 to 4 inches of rain to the Mogollon Rim of Arizona and 1 to 2 inches to the rest of the desert Southwest, Central Rockies and Great Basin.