It was just short of top-scale Category 5 hurricane with screaming 140 mph (220 kph) winds as it moved across the island, toppling telephone poles and fruit trees, shattering windows and tearing off the tin roofs of homes.
A Cuban television reporter on the Isla de la Juventud said the storm had felt like "the blast wave from a bomb."
"Buildings without windows, without doors," he said. "Few trees remain standing."
Cuban Civil defense chief Ana Isa Delgado said there were "many people injured" on the island of 87,000 people just south of the Cuban mainland, whose name means Isle of Youth. Nearly all its roads were washed out and some regions were heavily flooded.
"It's been very difficult here," she said on state television.
Gustav earlier killed 81 people by triggering floods and landslides in Haiti, the Dominican Republic and Jamaica. But in Cuba, none of the reported injuries were life-threatening.
The hurricane weakened slightly after crossing Cuba, slowing to Category 3 status Sunday. But it still packed top winds near 120 mph (195 kph) and forecasters predicted it would increase to a Category 4 before making landfall Monday along the U.S. Gulf coast.
More than 1 million Americans made wary by Hurricane Katrina took buses, trains, planes and cars as they streamed out of New Orleans and other coastal cities, where Katrina killed about 1,600 people in 2005.
That city's mayor, Ray Nagin, issued a mandatory evacuation order and warned that anyone found off their own property after it takes effect can be arrested. Police and National Guard troops were on the streets, preparing to patrol evacuated neighborhoods.
Nagin called Gustav the "mother of all storms" and told residents to "get out of town. This is not the one to play with."
In Cuba's Pinar del Rio, Gustav's massive center roared close to the community of Los Palacios, toppling electric towers and leveling homes. Highways were blocked by fallen trees and downed power lines, and all public transportation ground to a halt.
Hurricane-force winds stretched as far east as the capital, Havana, where streets were littered with branches and debris, power was knocked out and sheets of driving rain fell sideways for hours.
But by Sunday, no flooding could be seen in the central part of the city of 2 million people, and state radio said the damage was "minimal," although some areas remained without power and natural gas.
Public transportation began running again, as did buses and trains from Havana to the provinces. State radio said schools would open for the year as scheduled on Monday everywhere except Pinar del Rio.
In the fishing town of Batabano, 31 miles (50 kilometers) south of Havana, evacuees with children and dogs in tow returned to their pastel-colored, wooden homes to find many surrounded by knee-deep water. Some streets flooded, though residents were able to pedal bicycles through water that splashed up to the top of their tires.
"My house is full of water," said Aldo Tomas, 43, pulling palm branches from his living room. "But we expected more. We expected worse."
Tourist Lidia Morral of Barcelona, Spain, said Gustav forced officials to close beaches the couple wanted to visit earlier this week in Santiago, on the island's eastern tip. The storm also prevented them from catching a ferry from Havana to the Isla de la Juventud on Saturday.
"It's been following us all over Cuba, ruining our vacation," said Morral, who was in line at a travel agency, trying to make other plans. "They have closed everything - hotels, restaurants, bars, museums. There's not much to do but wait."
At 11 a.m. EDT Sunday, the U.S. hurricane center said Gustav was centered about 325 miles (520 kilometers) southeast of the mouth of the Mississippi River and moving northwest near 17 mph (28 kph).
Meanwhile, Tropical Storm Hanna was projected to move north of the Turks and Caicos Islands by late Sunday, then curl through the Bahamas by early next week before possibly threatening Cuba.
As it spun over open waters, Hanna weakened slightly and had sustained winds near 50 mph (85 kph) Sunday.