Playa de Carmen, a resort town across from Cozumel, was left without electricity and streets were largely empty as Rina swept the coast just 20 miles (30 km) west of Cozumel with winds of about 60 mph (95 kph).
The storm was moving north at about 7 mph (11 kph) and was expected to move inland and start weakening by early Friday.
Many tourists had already abandoned resorts around Cancun and the Riviera Maya ahead of what once threatened to be a Category 3 hurricane.
The Mexican Navy took mandatory evacuation orders so seriously that it sent boats to Holbox island, about 100 miles (160 kms) north of where the storm was expected to hit, to haul out by force about 80 residents who had refused to leave and hidden on the island during an earlier evacuation of about 2,300 people.
At least eight cruise ships changed itineraries away from the storm's path.
Lines snaked from ticket counters in Cancun's crowded airport Wednesday as jumbo airliners heading to Canada and Europe waited in pouring rain.
State Tourism Director Juan Carlos Gonzalez Hernandez estimated 10,000 tourists had left by Wednesday night.
NASA cut short an undersea laboratory mission near Key Largo, Florida, bringing the crew back to land.
Schools were ordered closed in communities along the coast and on Cozumel in anticipation of the storm.
Ports also closed to navigation for recreational, fishing and small boats in the state of Quintana Roo, home to Cancun, and neighboring Yucatan state, while the island of Cozumel was closed to larger vessels, including the ferry that connects the island and Playa del Carmen.
But some decided to ride out the weakened Rina. Early Thursday in Playa del Carmen, tourists and residents strolled along the promenade and the beach Thursday under cloudy but not-yet-rainy weather. At the beach, lifeguards were placing red flags warning people not to swim.
"We would prefer to lie on the beach and get in the ocean, but right now all we can do is walk around and go shopping," said Vera Kohler, a 27-year-old tourist from Frankfurt, Germany, who arrived Wednesday and planned to stay in the area until Sunday.
Domenico Cianni, a retired restaurateur from Vancouver, Canada, said he also prepared for a hurricane by buying extra food and beer and putting shutters on the windows of his rental home. But after hearing Rina had been downgraded to a tropical storm he decided to join tourists in Playa del Carmen's pier.
"We were curious about what's happening. We wanted to be part of the action," Cianni said.
A tropical storm warning was in effect for the Caribbean coast from Punta Allen to San Felipe.
Mexico's government said it was sending nearly 2,400 electrical workers plus cranes, vehicles and generators to repair and maintain services as quickly as possible after the storm.