Outlying sections of the storm also blew heavy rain across extreme South Texas on Wednesday, causing scattered power outages while many residents waited the storm out in shelters.
At 11 a.m. EDT, the storm was centered inland of Mexico's northeast coast, about 75 miles south-southwest of Brownsville, said the National Hurricane Center. It was moving toward the west at 10 mph.
A hurricane warning was dropped but a tropical storm warning was in effect for about 40 miles of the lower Texas coast from the Mexico border to Port Mansfield. Flood and tornado watches were posted for most of South Texas through midday.
The eye of the storm came ashore near San Fernando, Mexico, about 75 miles south of the U.S.-Mexico border, and about 85 miles south of Brownsville. Forecasters predicted the storm could dump up to 15 inches of rain as it moves inland over the mountains, causing flash flooding and landslides. There were no immediate reports of deaths or major injuries, but many small communities appeared to have been cut off by the storm.
It was weakening as it moved west, with maximum sustained winds of 105 mph. A gust to 49 mph was reported in Brownsville, the hurricane center said.
In San Fernando, a community of 60,000 slightly inland, the storm shredded metal roofs and shattered a bank's plate-glass windows, leaving window blinds to dance in the wind.
The American Red Cross estimated about 4,000 people packed up their televisions, video games and coolers of drinks and snacks and settled into the 14 shelters set up across south Texas.
"Why take a risk?" asked Zulema Longoria, 43, one of about 160 people spending the night at a shelter in Elma E. Barrera Elementary.
Cindy Ruiz went to the school with 12 relatives, including her husband and eight children.
Outside, school buses were lined up in case flooding made it necessary to take the storm refugees farther inland.
Nearly 13,000 customers were without electricity, about half in Harlingen and others in the coastal towns of Port Isabel and South Padre, said Larry Jones, spokesman for the utility AEP Texas. Service should be restored during the afternoon, he said.
Another 10,000 were reported without power in Brownsville.
Emily's landfall Wednesday marked the second time in three days the storm had hit Mexico. It slammed into the Yucatan Peninsula on Monday, ripping the roofs off resort hotels and stranding thousands of tourists along the popular Mayan Riviera, which includes the resort of Cancun.
Officials in Mexico's Tamaulipas state, which borders Texas, said 18,000 people had been evacuated Tuesday from 20 low-lying, seaside communities — including nearly everyone from Carbonera, a tiny fishing hamlet that appeared to have taken a direct hit from the storm. Only 13 people refused to leave.
Army trucks roamed the streets of small Mexican fishing villages Tuesday afternoon, collecting evacuees laden with suitcases and rolled-up blankets. In southern Texas, giant waves gobbled up stretches of beach, and about 4,000 people spent the night in 14 shelters.
In the beachside community of Carbonera, the few residents left Tuesday night were holed up indoors, hiding from authorities desperate to move them to safety. Cowering dogs were all that could be found on the streets, while a lone cat sought refuge from the rain in the doorway of an abandoned grocery store — its shelves stripped of food and supplies.
Some 150 miles south, in another Mexican community that was evacuated, La Pesca, residents were taken to a naval base on a relatively high point on the edge of town. There, excited children raced giddily about, shrieking and laughing as their parents settled in.
In another part of town, 67-year-old fisherman Felipe Portillo helped his sons haul five small, fiberglass fishing boats off the beach and up to the roadside, away from the water.
"Overconfidence kills men," Portillo said. "Running is your best defense."
Javier Hurtado, a maintenance worker at one of South Padre Island's high-rise condominiums, said the wind made his 20-mile drive from his home in Los Fresnos a challenge.
"It's pretty bad on the highway right now," he said. "I thought I was going to have to pull over because it was so windy."
But other motorists told Michael Board of CBS radio affiliate KTSA "they didn't think it was that bad. They rode in expecting a lot more from this storm. They said, 'It's just some wind and rain.'"
However, the winds on South Padre Island were strong enough to rip the plywood boards of several buildings and "it even pulled the stucco siding off a swimwear store here. Driving by a gas station here, I see that the wind has ripped off the metal siding that surrounded the island around the gas pumps," Board reported.
Meteorologists said 2 to 4 inches of rain could fall in the parched lower Rio Grande Valley.