The government announced it was stepping up emergency production of bread at state-run bakeries and lines formed all over the city as Cubans waited for loaves.
In tourist-friendly Old Havana, heavy winds and rain battered crumbling historic buildings. There were no immediate reports of major damage, but a scaffolding erected against a building adjacent to the Plaza de Armas was leaning at a dangerous angle.
Lidia Morral and her husband were visiting Cuba from Barcelona. She said Gustav forced officials to close the beaches the couple wanted to visit 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."
On Cuba's Isla de Juventud, Gustav toppled trees and was peeling back the roofs of some houses on Saturday.
"The rain is not so intense, but there is a lot, a lot of wind," said Isabel Alarcon from Nueva Gerona, the largest city on the island of 87,000 people. "The officials, they have told us the wind will be bad first but then the rain could cause flooding into the night."
By late Saturday afternoon, Gustav was about 80 miles (135 kilometers) south-southwest of Havana and it was moving northwest near 15 mph (24 kph).
Hurricane force winds extended out 70 miles (110 kilometers) in some places.
The US naval base at Guantanamo, Cuba, was hundreds of miles (kilometers) to the east, out of the storm's path.
In the Gulf of Mexico, where about 35,000 people work staffing offshore rigs and production facilities, among other tasks, oil companies wrapped up evacuations in preparation for the storm.
As of midday Saturday, more than three-fourths of the Gulf's oil production and nearly 40 percent of its natural gas output had been shut down, according to the US Minerals Management Service, which oversees offshore activity.
The US Gulf Coast accounts for about 25 percent of domestic oil production and 15 percent of natural gas output, according to the MMS. The Gulf Coast also is home to nearly half the nation's refining capacity.
Analysts say prolonged supply disruptions could cause a sudden price uptick for gasoline and other petroleum products.
On Friday, Gustav rolled over the Cayman Islands with fierce winds that tore down trees and power lines while destroying docks and tossing boats ashore, but there was little major damage and no deaths were reported.
Haiti's Interior Ministry on Saturday raised the hurricane death toll there to 66 from 59 and Jamaica raised its count to seven from four. Gustav also killed eight people in the Dominican Republic early in the week.
Meanwhile, the hurricane center said Tropical Storm Hanna was projected to near the Turks and Caicos Islands late Sunday or on Monday, then curl through the Bahamas by early next week before possibly threatening Cuba.
As it spun over open waters, Hanna had sustained winds near 50 mph (85 kph) late Saturday afternoon and the hurricane center warned that it could kick up dangerous rip currents along parts of the southeastern US coast.