Defending champion Victoria Azarenka recovered from a stuttering start to see off the brave challenge of Svetlana Kuznetsova.
An upset seemed to be on the cards as Kuznetsova opened up a 4-1 lead, however Azarenka moved through the gears to claim 12 of the next 14 games to win 7-5 6-1.
Azarenka said: "She played really well throughout the whole match.
"I know what kind of tennis she is capable of and in the beginning it took a little bit of adjustment because she has a very different game.
"I am glad I could produce my best tennis when it was needed."
Kuznetsova had showed glimpses that took her to two grand slam titles of her own - the US Open in 2004 and the French Open in 2009.
Kuznetsova, whose 2012 campaign was ravaged by a serious knee injury, had caught Azarenka cold as she mixed creativity with raw power.
However Azarenka came roaring back into the match and the turning point came when she broke in the seventh game.
The momentum was very much with the world No 1 and she broke again in the 11th game before serving out for the set.
Azarenka broke for a third time at the start of the second set and although Kuznetsova levelled immediately that was as good as it got for the Russian. Azarenka rattled off five games on a bounce to advance to the semi-finals, where she will face Sloane Stephens.