Williams has now beaten Sharapova 18 times in row, and Sharapova has not defeated Williams since 2004.
Williams also has won 16 consecutive sets against Sharapova, who last won a set against Williams in 2013.
Sharapova got off to good start Tuesday, taking an early 2-0 lead in the opening set, but Williams controlled things from there. The American got ahead 5-4 and closed out the set on her fourth set-point opportunity.
Williams raced to a 5-0 lead in the second set and eased to victory over Sharapova, who won five Grand Slam singles titles
"It was super intense. She's an incredibly intense, focused player who was No.1 and who's won so many Grand Slams for a reason," Williams said. "You have to come out with a lot of fire and intensity ... I think I didn't start out that way."
The match stats bore out Williams' usual dominance: a 31-11 edge in winners and a 13-3 margin in aces.
Next up in her bid for a 22nd grand slam title, Williams will face Agnieszka Radwanska of Poland in the semifinals.
The fourth-seeded Radwanska advanced by beating 10th-seeded Carla Suarez Navarro of Spain 6-1, 6-3 in a quarterfinal match.
Radwanska benefited from 45 unforced errors by Suarez Navarro, while the Pole gave away just 13 points.
A Wimbledon finalist in 2012, Radwanska is in a Grand Slam semifinal for the fifth time in her career. She also reached the semis in Australia two years ago.
"Right now I have nothing to lose," Radwanska said. "Hopefully (I will) play my best tennis, otherwise I'll be in big trouble."
In men's singles quarterfinals later Tuesday, top-seeded Novak Djokovic of Serbia plays seventh-seeded Kei Nishikori of Japan, and third-seeded Roger Federer of Switzerland plays sixth-seeded Tomas Berdych of the Czech Republic.