errors to begin the match, hitting a backhand crosscourt wide on breakpoint to drop her opening serve. However the American immediately broke the Russian's serve to pull even at 1-1.
The players remained on serve to enter the first set tiebreaker.
Williams, made to run in the tiebreaker by deep Dementieva groundstrokes, turned in six errors to fall behind 3-6 in the tiebreaker. Dementieva doublefaulted on setpoint number one before Williams sent a forehand down the line return of serve wide to fall behind 6-7.
The American raced to a 3-1 second set lead behind steadier play before dropping three games in a row to trail 3-4 after experiencing several games of forehand inconsistency.
Williams broke serve at 5-5 before striking two aces in a row to take the second set 7-5.
But Williams, struggling all day with her consistency, continued to add an increasing amount of topspin to her groundstrokes in the place of her normally more frequently seen powerful flat groundstrokes.
A short Williams forehand netted on breakpoint sent Dementieva ahead in the decisive set 3-1.
Williams broke back to reach 3-3 before again falling behind 4-5 after several more errors. A backhand down the line volley winner from Williams saved matchpoint before the American held serve to pull even at 5-5.
With Dementieva serving at 6-6, Williams connected with several powerful groundstrokes including an inside out backhand down the line winner on breakpoint for a 7-6 lead.
In the final game, more consistent play from Williams earned her a hold of service and a Saturday championship round berth.
Williams would finish the 2 hours and 49 minutes match with 20 aces.