Serena Williams beats Sharapova in Madrid quarters
Earlier in the Spanish capital, Azarenka overcame a shaky start to beat French Open winner Li Na 3-6, 6-3, 6-3.
Williams opened strong, hitting six aces and earning two early breaks to take the first set against the second-ranked Russian.
Sharapova finally showed some fight and broke for love to even the score at 2-2 in the second set, but she quickly squandered her break with a costly sixth double fault to fall behind for good.
Williams, who improved to 11-0 on clay this year, will face either U.S. Open champion Sam Stosur or Czech Lucie Hradecka.
After Azarenka struggled on serve early on, last year's runner-up found her stride and broke her Chinese opponent's first two service games of the second set en route to pulling even at a set each.
Azarenka, who has won four titles this season, then used her powerful groundstrokes to jump out to an insurmountable 4-0 lead in the decider before holding off Li's late charge.
The Belarusian will face the winner of the quarterfinal between Agnieszka Radwanska and Varvara Lepchenko.
On the men's side, Argentina's Juan Martin del Potro beat Alexandr Dolgopolov of Ukraine 6-3, 6-4 to move on to a semifinal with either Tomas Berdych or Fernando Verdasco.
Later, top seed Novak Djokovic played Serbian countryman Janko Tipsarevic before Roger Federer faced David Ferrer.
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