Victoria Azarenka (Photo: Reuters)
The Belarussian, runner up in Madrid last year, looked to be cruising at 4-1 up in the third before China's Li broke back. Li was unable to take advantage of four break-point chances, however, and 36 unforced errors told its own story.
Azarenka will face newly-installed world number three Agnieszka Radwanska or American qualifier Varvara Lepchenko in the last four.
Former world number ones Serena Williams and second seed Maria Sharapova follow next on centre court. Fifth-seed Samantha Stosur takes on another qualifier Czech Republic's Lucie Hradecka in the other quarter-final.
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