Ernesto weakened to a tropical depression as it moved inland early Friday, though forecasters warned it could still dump dangerous rains in the mountains of Mexico's flood-prone southern Gulf region.
In Tabasco state, two fishermen drowned when the stormed passed through the area Thursday, Gov. Andres Granier told reporters.
Granier said the storm's strong winds ripped rooftops from several homes but residents refused to evacuate, fearing their possessions might be stolen. "People have chosen to stay in their homes and we are helping them," he said.
Ernesto came ashore near the waters dotted with oil rigs operated by the state oil company in the far southern Gulf of Mexico. The government closed its largest Gulf coast port, Veracruz, and the smaller ports of Alvarado and Coatzacoalcos.
Coatzacoalcos, a major oil port, got seven inches of rain in the 24 hours before Ernesto's center passed just a few miles away, according to Mexico's weather service. San Pedro in the neighboring state of Tabasco had seen more than 10 inches.