Officials released water from an Isaac-stressed dam at a lake near the Louisiana-Mississippi border, hoping to ease the pressure as the storm soaked Louisiana for yet another day, flooding homes and forcing last-minute evacuations and rescues.
New Orleans itself was spared, thanks in large part to a levee system fortified after Katrina devastated the Gulf Coast in 2005.
Forecasters expected Isaac to move farther inland over the next several days, dumping rain on drought-stricken states across the nation's midsection before finally breaking up over the weekend.
As the storm slogged its way across Louisiana and windy conditions calmed Thursday, the extent of some of the damage became clear.
Hundreds of homes, perhaps more, were underwater, thousands of people were staying at shelters and half of the state was without power. About 500 people had to be rescued by boat or high-water vehicles, and at least two people were killed. And the damage may not be done.
Besides releasing water from the dam at the Louisiana-Mississippi border, hoping to ease the pressure, they also started work on a levee breach in hard-hit Plaquemines Parish in Louisiana.
In Arkansas, power lines were downed and trees knocked over as Isaac moved into the state.
Farther south, where evacuations were ordered ahead of the storm, Isaac's unpredictable, meandering path and the amount of rain — as much as 16 inches (41 centimetres) in some places — caught many off guard.
Eric Blake, a hurricane specialist at the National Hurricane Center in Miami, said although Isaac's cone shifted west as it zigzagged toward the Gulf Coast, forecasters accurately predicted its path, intensity and rainfall.
He did say the storm crept ashore somewhat slower than anticipated. Blake also said local officials and residents shouldn't use Katrina as a guide for what areas were at the greatest risk of flooding during Isaac.
"Every hurricane is different," Blake said. "If you're trying to use the last hurricane to gauge your storm surge risk, it's very dangerous."
Along the shores of Lake Pontchartrain near New Orleans, officials sent scores of buses and dozens of high-water vehicles to help evacuate about 3,000 people as rising waters lapped against houses and left cars stranded.
Floodwaters rose waist-high in some neighbourhoods, and the Louisiana National Guard was working with sheriff's deputies to rescue people stranded in their homes.
A Coast Guard helicopter hoisted a couple and their dogs early Thursday from a home in LaPlace, between the Mississippi River and Lake Pontchartrain, after storm surge poured into their neighbourhood and local authorities called for help. The couple was taken to New Orleans and reported in good condition.
"The husband and wife and their two dogs were in an area where a lot of houses washed away," said Lt.Cmdr. Jorge Porto.
To the east, evacuations were ordered in a sparsely-populated area as the lake dam threatened to break.
Officials in Tangipahoa Parish, Louisiana, feared the water would pour into the already swollen river and flood places downstream.
Louisiana Gov. Bobby Jindal said the controlled release should prevent a significant flooding event. A tow truck driver was killed Thursday morning when a tree fell on his truck in Picayune, Mississippi, just across the state line from Louisiana.
In Vermilion Parish, a 36-year-old man died after falling 18 feet (5.5 metres) from a tree while helping friends move a vehicle ahead of the storm. Deputies did not know why he climbed the tree.
President Barack Obama declared federal emergencies in Louisiana and Mississippi late Wednesday, allowing federal aid to be freed up for affected areas.
In Plaquemines Parish, a sparsely populated area south of the city that is outside the federal levee system, dozens of people were stranded in flooded coastal areas and had to be rescued.
The storm pushed water over an 18-mile (29-kilometre) levee and put so much pressure on it that authorities were intentionally puncturing the floodwall to relieve the strain.
More than 900,000 homes and businesses around the state — about 47 per cent of all customers — were without power Thursday. Utility company Entergy said that included about 157,000 in New Orleans. Isaac became a tropical depression, meaning its top sustained winds dropped below 39 mph (62 kph).
The storm's centre was on track to cross Arkansas on Friday and southern Missouri on Friday night, spreading rain as it goes.
Isaac came ashore late Tuesday as a Category 1 hurricane, with 80 mph (130 kph) winds near the mouth of the Mississippi River. It drove a wall of water nearly 11 feet (3.4 metres) high inland.
With files from CNN