The Russian player, ranked fourth in the world, struggled in the first set, but settled into her game in the second, beating the unseeded Chan.
"She was on fire at the beginning and put a lot of pressure on me,'' Dementieva said. "I didn't expect such a high level and it took me a while to get into the game.''
Second-seeded Caroline Wozniaki of Denmark needed only 56 minutes to beat Alberta Brianti of Italy 6-1, 6-0. Wozniaki served three aces and won 80 percent of first serve points.
"I knew it was going to be tough, but I just managed to win the important points and push her the way I wanted,'' Wozniaki said.
Eighth-seeded Carla Suarez Navarro of Spain also had an easy passage to the second round Tuesday, beating Nathalie Dechy of France 6-4, 6-0.
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