Rita made landfall at 3.30am (0730 GMT) as a Category 3 storm just east of Sabine Pass, on the Texas-Louisiana line, bringing top winds of 193kph and warnings of up to 64cm of rain, the National Hurricane Centre said.
But by late morning, it had weakened to Category 1 status, with its sustained winds at 121 kph as it moved north.
Fears of severe flooding persisted. Parts of the east Texas counties of Jasper and Tyler had received 25cm to 30cm of rain, the National Weather Service said.
There were no immediate reports of fatalities or any detailed word on damage to the area's vast oil refinery industry, although rescuers and search teams in many areas had to wait for winds to subside before venturing out.
About 3 million people had fled an 800km stretch of the Texas-Louisiana coast ahead of the storm, motivated partly by the devastating toll that Hurricane Katrina inflicted on New Orleans and other parts of the Gulf Coast barely three weeks ago.
The storm spun off tornadoes as it churned northwest, causing transformers to explode. In Jasper County, a house with seven people inside floated in floodwaters after it came off its foundation, said sheriff's communications supervisor Alice Duckworth.
Waves crash over a fishing pier
in Galveston, Texas
But the flood-prone cities of Houston and Galveston escaped a direct hit.
"So far, Houston is weathering the storm," mayor Bill White said on Saturday.
New Orleans flooding
In New Orleans, rain drenched parts of the abandoned city early on Saturday, straining the levee system damaged by Katrina and causing more flooding in ruined and abandoned poor neighbourhoods.
But the forecast of up to 8cm throughout the day was less than had been earlier predicted.
"Overall, it looks like New Orleans has lucked out," National Weather Service Meteorologist Phil Grigsby said.
Heavy rain fell south of New Orleans in low-lying Jefferson Parish, where a tidal surge of about 2m swamped some neighbourhoods.
Residents of Lafitte, a town of 1600 south of New Orleans, were being evacuated by bus.
A firefighter battles a blaze in
Galveston, Texas, after Rita hit
Some of the worst early damage reports were out of Vinton, where fires were burning, the roof was torn off the town's recreation centre and homes were damaged by fallen trees, Lieutenant Arthur Phillips said.
In Lake Charles, home to the nation's 12th-largest seaport and refineries run by ConocoPhillips, ExxonMobil, Citgo and Shell, nearly all 70,000 residents had evacuated.
Louisiana governor Kathleen Blanco said more than 90% of residents in southwestern parishes, about 150,000 people, had evacuated.
Fires were reported in and around Houston, including one in a two-storey apartment building in southeast Houston that left eight units damaged, the authorities said.
Nobody was hurt, according to district chief Jack Williams.
Several buildings were damaged or destroyed by fire in Galveston, and a blaze broke out before dawn at a shopping complex in Pasadena. There were no immediate reports of injuries.
As the sun came up in downtown Beaumont, a port city of 114,000, the few people who stayed behind emerged to find some blown-out windows, damaged roofs, signs twisted and lying in the street and downed trees.
George Bush being briefed at the
US Northern Command in Colorado
The wind was still gusting, but nothing like the 160-kph winds that ripped through early on Saturday morning. A light rain was falling.
As the storm raged, the torches of oil refineries could be seen burning in the distance from downtown Beaumont.
Officials had worried about the storm's threat to those facilities and chemical plants strung along the Texas and Louisiana coast.
The facilities represent a quarter of the nation's oil refining capacity, and business analysts said damage from Rita could send gas prices as high as $4 a gallon. Environmentalists warned of the risk of a toxic spill.
In the days before the storm's arrival, hundreds of thousands of residents of Texas and Louisiana fled their homes in a mass exodus that produced gridlock and heartbreak.
South of Dallas, a bus of Rita evacuees caught fire in gridlocked traffic, killing as many as 24 nursing home residents who thought they were getting out of harm's way.
Grocery shelves were emptied, petrol stations ran out of fuel and motorists had to push their cars to the side of highways after idling for hours in stuck traffic and running out of gas.
White, the Houston mayor, expressed frustration: "It is just totally unacceptable that there was not adequate fuel supplies stashed around the state."
Houston streets were all but
deserted after evacuations
President George Bush, mindful of criticism the federal government was slow to respond to Katrina three weeks ago, planned to visit his home state of Texas on Saturday. He will go to the state's emergency operations centre in Austin and then to San Antonio.
"The past three weeks have tested our nation and revealed the strength and resilience of our people," he said in his weekly radio address.
"The courageous spirit of America will carry us through any storm, and the compassionate soul of our nation will help us rebuild."