Williams continued her dominance in the second set, breaking Wozniacki in the first and third games to go up 4-0. The Dane fought back, closing the gap to 4-3, but it was not enough to stop Williams from winning the set 6-4.
"I felt I played really well tonight, especially in the first set," Williams told reporters. "I played well in the second set too, but I think Caroline just played so much better and she lifted her game so much.
"But I think overall it was the best performance I've had this week, which I'm excited about."
Third-seeded Agnieszka Radwanska will be up next for Williams, who took her number of wins in 2013 to 71.
Ninth-seeded Czech Petra Kvitova broke the hearts of the crowd when she rallied to beat home favourite Li Na, seeded fourth, 4-6 6-2 6-4.
The former Wimbledon champion set up a semi-final date with Serbian Jelena Jankovic, who won a two-hour, 36-minute match against Czech Lucie Safarova 6-7(3) 6-4 6-4.
Radwanska, who has never beaten Williams in their previous six meetings, defeated seventh-seeded German Angelique Kerber 7-6(7) 6-4 to complete the semi-final line-up.
(Reporting by Sudipto Ganguly in Mumbai; Editing by Clare Fallon)
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