After taking the first set in 30 minutes behind a blistering forehand, the second-seeded Russian quickly went up 3-0 in the second set before faltering. Tanasugarn suddenly came to life, breaking in the fourth game and winning five of the next seven games to make it 5-5.
Sharapova dug in during the 11th game, however, breaking again and then closing the match with an ace at a covered Ariake Colosseum.
"I served really well today," Sharapova said. "It was important for me to serve well because she reads the ball really well. I had a bit of letdown in the second set. She started playing really well. I was glad I was able to come back and win it in two sets."
Sharapova said the players are happy to support this tournament following the March 11 earthquake and tsunami.
"The commitment the players have shown is incredible," she said. "With nearly a full draw, I think the players have shown their dedication."
The annual WTA Tour tournament is normally outdoors, but late-morning rain forced the closure of the roof over the main court and suspension of play on outdoor courts.
Bartoli defeated Ayumi Morita of Japan 6-3, 0-6, 6-3, and Jankovic beat Barbora Zahlavova Strycova of the Czech Republic 6-4, 6-2.
Bartoli prevailed in a baseline battle despite a second-set whitewash. She overpowered Morita with a strong backhand in a final set featuring service breaks in the first three games. Morita committed several unforced errors in the third set, leading to her defeat. Serving to stay in the match, Morita staved off four match points before succumbing.
Defending champion Caroline Wozniacki of Denmark, seeded first in the $2 million tournament, has a first-round bye and on Tuesday plays the winner of the match between Rebecca Marino of Canada and Jarmila Gajdosova of Australia.