Packing winds of up to 125 mph, Damrey made landfall north of Hainan's Wanning City before dawn, the official Xinhua News Agency said. It was the island's strongest typhoon since 1973, the agency said.
The storm, whose name means "elephant" in Cambodian, scoured the island's southern portion before heading out to sea to toward Vietnam (search) to the west. More than 200,000 people were being evacuated along the coast ahead of its expected arrival Tuesday, Xinhua said, citing Vietnamese officials.
Both victims were women who died in Wanning as they were preparing to flee, according to Xinhua.
Zhong Yueqin, 62, was trying to retrieve a TV set from inside her house when it collapsed on top of her, while Li Ruju, 42, was killed by a falling wall while closing up her house, it said.
Hotels in the Yalong Bay resort district were largely empty, with lingering tourists barricading themselves in their rooms, according to receptionists at the lodgings. The Sheraton (search) and Marriott (search) resorts were operating with minimal staff, with many employees unable to get to work, the receptionists said.
"There aren't many people coming in," said a receptionist at the Sheraton, who refused to give her name because she was not authorized to comment. She said she had no information on damage to the hotel.
One of China's poorest regions, Hainan has in recent years marketed itself as "China's Hawaii," cashing in on its tropical climate, pristine beaches and the colorful cultures of hill tribes living in its mountainous center.
Flights in and out of Sanya's Phoenix International Airport were canceled from Sunday evening, said a woman who answered the phone at the airport's customer service desk.
The airport was advising passengers not to buy tickets for flights before Wednesday, said the woman, who gave only her surname, Huang.
The typhoon also knocked out power to most of Hainan's 8 million people, Xinhua said. Rice fields were flooded, and fruit and rubber trees were damaged or destroyed. Strong winds and rain struck areas as far away as Hong Kong (search), about 370 miles to the northeast.
While still a tropical storm in the Philippines last week, Damrey triggered rain that killed at least 18 people.