hour and 15 minutes of play.
Kvotova held serve then broke serve to jump ahead early in the final set 2-0. However after hitting her 6th doublefault of the day, the Czech would lose serve to put the set back on serve at 2-1.
A Williams doublefault on breakpoint in the following game sent Kvotova ahead 3-1. The Czech would then hold serve to increase her lead to 4-1.
In the next two games, Williams held serve then broke serve to return the set back on serve at 4-3.
Aces number ten and number eleven of the day from the American would level the set at 4 all.
In the following game, Kvotova held serve on game point with an ace of her own to lead 5-4.
However a second serve ace on game point from Williams; her 13th ace of the day, would again level the set; this time at 5 all.
Williams would then break serve before connecting with her 14th ace of the day to end the quarterfinal encounter after two hours and seven minutes of play.
In semifinal number two Saturday, the 31 year old American takes on the third seeded Maria Sharapova of Russia. To start the day, the current world number one Victoria Azarenka of Belarus will meet the fourth seeded Agnieszka Radwanska of Poland in semifinals number one. In the United States, the Tennis Channel will televise both semifinals as well as Sundayís final by tape delay.
Williams could have returned to the top ranking in January following the Australian Open. But the American suffered a twisted then swollen ankle as well as a back injury which hampered her performance in Melbourne.
Last year Williams won Wimbledon, the Olympics, the US Open as well as the WTA Tourís year end championships tournament.