It was expected to sweep across a sparsely populated stretch of the peninsula, and then make a second landfall Saturday night in northwestern Mexico's mainland -- possibly as a hurricane, the U.S. National Hurricane Center said.
Baja residents fled to shelters as floodwaters rose in their homes. Winds bent palm trees and some streets were in knee-deep water in the town of Puerto San Carlos.
"We left our house because we were scared. Our house is pretty poor and the water was already coming in," said Maria Espinosa, 54, who arrived at a high school with her daughter and two grandchildren. They joined about 60 other people sitting on foam mattresses and blankets.
A hurricane warning was issued for the west coast of Baja California from Puerto San Andresito to Agua Blanca. The government also issued hurricane warnings along the coast of the border state of Sonora and on the east coast of the Baja peninsula from near La Paz north to Loreto.
As of 11 a.m. EDT (1500 GMT), the hurricane's center was located about 45 miles (70 kilometers) south of Cabo San Lazaro, Mexico, and was moving north-northeast at 15 mph (24 kph).
The storm's remnants were expected to dump more rain on water-logged West Texas, where authorities were preparing for more flooding.
State and local officials plan to activate an emergency operations center Monday in Presidio, where an earthen levee is struggling to hold back the swollen Rio Grande.
The Governor of Baja California Sur state, Narciso Agundez, said officials here are "very worried."
Meanwhile, Tropical Storm Odile hugged the southwest coast of Mexico.
Flooding in Acapulco forced officials to cancel classes at schools. Civil Protection officials in Guerrero state urged about 10,000 people living along river banks or other dangerous areas to evacuate.
Mudslides and fallen trees blocked roads, and 150 homes were under 13 feet (4 meters) of water in El Paraiso, a small town north of Acapulco.
Odile was located about 60 miles (100 kilometers) southwest of Zihuatenejo, a resort town north of Acapulco and was moving northwest at about 13 mph (20 kph). Odile could become a hurricane, and a small deviation in its path could bring the storm inland, the hurricane center said.
A hurricane watch was in effect from Manzanillo to Zihuatanejo, a resort town north of Acapulco. A tropical storm warning was in effect from Tecpan de Galeana to Manzanillo, as Odile moved parallel to the Pacific coast with winds of about 65 mph (100 kph).