Fourth seeded Sharapova committed six double faults compared to two by Kaia Kanepi but still downed the Estonian 6-4 6-1 in 90 minutes.
Sixteenth seeded Williams shrugged off a slow start to overcome Heather Watson 6-3 6-1 in their first encounter.
"Heather was playing really well," seven-times grand slam winner Williams, who dropped the first three games in the opening set, said of her opponent.
"I mean, the first games she didn't miss a serve for six points. I give her a lot of credit," said the American who faces 12th seed Ekaterina Makarova in the second round.
Russian Makarova had to work harder for her 6-7(8) 6-4 6-4 win against Spaniard Garbine Muguruza.
Australian Samantha Stosur beat Francesca Schiavone 6-4 6-2 to set up a second round clash against former world number one Caroline Wozniacki who is eyeing a spot in the year ending WTA Finals in Singapore.
From 3-4 in the first set, Australian Stosur went on to win eight of the next nine games before eventually beating the Italian, her conqueror in the 2010 French Open final, in 92 minutes.
Wozniacki got one of the four first round byes for making the semi-finals at the Wuhan Open and is in contention for one of the last four spots in the year ending WTA Finals in Singapore.
In other matches, second seed Simona Halep beat Czech Barbora Zahlavova Strycova 6-1 6-4, while Japan's Kurumi Nara humbled 11th seeded Italian Sara Errani 3-6 6-3 6-4.
(Reporting by Amlan Chakraborty; editing by Alan Baldwin)
Share
