The storm, named Isidore, dumped torrential rains on low-lying coastal settlements, including the famed French Quarter of New Orleans.
Residents of Grand Isle, at the southern tip of Louisiana, suffered the extremes of the bad weather, recording floods 1.2 metres (4 feet) deep early on Thursday before the waters receded later in the day.
The National Hurricane Centre said it feared the rainfall could cause "life-threatening floods".
Early this week Isidore's hurricane-strength winds battered Mexico's Yucatan peninsula, killing four people - and leaving seven fishermen unaccounted for.
But during the storm's passage across the Gulf of Mexico it has lost some of its force.
That did not prevent authorities enforcing a mandatory evacuation of 16,000 people in coastal communities.
Eye of the storm
The storm swept in over south-eastern Louisiana early on Thursday, prompting the highest tides in 20 years and fears of severe erosion.
At 1100 (1500 GMT), the storm was tracking north-north-east at an average speed of 22.5 kilometres per hour (14 mph).
Winds were averaging 97 kph (60 mph), with sustained faster gusts.
About 34,000 homes in Louisiana remain without power, an emergency official told Reuters news agency.
To the east of Louisiana, in Alabama and Mississippi, states of emergency were in effect. And the National Guard was on alert.
Hardy regulars
In New Orleans, authorities issued an overnight curfew late on Wednesday and many stores had boarded up windows and sandbagged the doors.
But a few hardy regulars were still to be seen in the bars and cafes that kept the beer taps running.
Isidore is forecast to weaken as it moves inland, but will still threaten rainfall of 26-51 centimetres (10-20 inches).
A tropical storm warning remains in effect from Texas to Florida.
Meanwhile, tropical storm Lili lost most of its clout and was downgraded to a tropical depression. Haiti, the Dominican Republic and Jamaica lifted storm alerts.