Sharapova had conceded only nine games coming into the match but Asia's first grand slam singles champion broke the Russian three times to capture the first set and twice in the second to serve for the match at 5-2.
With the temperature rising above 34 Celsius (93F), the 30-year-old Chinese kept her cool to close out the match in one hour and 33 minutes on the second match point when Sharapova clubbed a return into the net.
Li, also a finalist in 2011, will play Victoria Azarenka or Sloane Stephens in the final.