It was a better start than last year at the Family Circle, where Williams had to withdraw after a groin pull in her first match.
The fifth-seeded Williams, who has won 29 tour titles, got off to a slow start on Tuesday. She was broken in the first game, which began with a double fault. But she settled down, mastering her serve and scattering five aces through the match.
"I got a slow start in general. It was cold and it was just a late match. So those are just the excuses that I'm giving myself as to why I served bad," said Williams, who is ranked No. 9 in the world.
The stadium court match ended about 10 p.m. with temperatures in the upper 40s.
Williams said Dulko, ranked No. 48 in the world, gave her some trouble with the variety in her game.
"She would hit a winner and then she would hit really soft balls and then she would hit a drop shot and a slice," Williams said.
Earlier Tuesday, unseeded Sorana Cirstea upset third-seeded Anna Chakvetadze 6-2, 1-6, 6-2 in a second round match.
Cirstea, an 18-year-old Romanian who has never won a WTA event, is ranked 86th. Her best finish was second in Budapest last year.
"Up until now, I actually believed hard courts were my best surface but now I think I'm going to change my mind," said Cirstea, who has now won consecutive three-set matches on the green clay at the $1.3 million tournament.
Chakvetadze, a Russian ranked No. 6 in the world, won her seventh tour title indoors at Paris earlier this year and faced Cirstea on a blustery afternoon. Temperatures were in the high 50s and winds gusted to more than 30 mph, but Chakvetadze wasn't blaming the conditions.
"She just pushed the ball back and I made mistakes," she said. "I think it's just the way I'm playing right now."
Earlier, eighth-seeded Dinara Safina of Russia advanced by defeating Lourdes Dominguez Lino of Spain 6-1, 6-4 in a second-round match. And Agnes Szavay of Hungary, seeded 10th, defeated Ai Sugiyama of Japan 7-5, 3-6, 6-4.
Victoria Azarenka of Belarus, the 13th seed, defeated Chanelle Scheepers of South Africa 6-1, 6-0, while Dominika Cibulkova of Slovakia, seeded 15th, retired with a lower back injury during her match with Anastasia Rodionova of Russia, who was up 6-4, 1-0.