The slow-moving system, downgraded to a tropical storm, threatened to keep churning for another day. Hurricane warnings and watches were discontinued.
Dozens of families that had ignored mandatory evacuation orders in a low-lying area retreated to their attics and roofs and sought rescue amid the howling wind and pounding rain.
The punishing conditions will persist "all day today, into tonight, into tomorrow," said Richard Knabb, director of the National Hurricane Center.
While barely at hurricane strength, Isaac was creeping across the region at only 6 miles per hour, giving it a long time to inflict damage.
Gov. Bobby Jindal said there was a report of a fatality in a fire early Wednesday, but officials had not confirmed the report.
Officials were quick to emphasize that the huge federal investments in recent years to avoid a repeat of Hurricane Katrina's horror had worked.
"The system that the country invested in is absolutely paying off," said Louisiana Sen. Mary Landrieu.
Despite the "terrible, determined, and nasty storm," there has been "no massive and catastrophic flooding," Landrieu said, crediting "the extraordinary investments."
"There is no evidence of any (water) overtopping (canals)" in the city, said the senator's brother, New Orleans Mayor Mitch Landrieu. "We have full confidence the levees will hold."
But in nearby Plaquemines Parish, a levee overtopped, creating a kind of flooding the parish did not see even during Hurricane Katrina, which hit seven years ago Wednesday.
More than 150 calls came in to 911 from people wanting to be rescued, said Terry Rutherford, commander of authorities in Plaquemines Parish.
By mid-morning, 75 people had been rescued from flooded homes and rooftops in Braithwaite in Plaquemines Parish, CNN affiliate WWL reported. At least 25 others were awaiting rescue on the parish's east bank, the report said, citing parish President Billy Nungesser.
Emergency management officials reported the overtopping of an 18-mile stretch of the back levee from Braithwaite to White Ditch, according to the the National Weather Service office in New Orleans.
The levee is maintained by the parish and is not part of the federal hurricane protection levee system, according to office.
Katrina breached the levee in two places, the Army Corps of Engineers said.
"It's very unfortunate that people did not heed the warnings," Mary Landrieu told CNN, adding, "our hearts go out" to them.
"Now the Coast Guard's got to go out with winds still gusting 60 to 70 miles per hour in some areas" to save them, she said.
The New Orleans levee system and pump stations were working furiously to deal with the deluge.
The system was rebuilt and reinforced at a cost of $14 billion after it failed when Katrina struck in 2005. Nearly 1,800 people died as a result of that storm, the majority when levees failed and flooded.