Williams will now meet fellow American Madison Keys in the semi-finals.
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The American dominated from the outset in her 6-2, 6-2 win, and only had to wait until the third game of the match to break Cibulkova’s serve.
A nervy Cibulkova struggled with Williams’ power game, and the Slovak had her serve broken yet again in the fifth game and she went on to lose the first set 6-2.
Cibulkova – who reached the final of the Australian Open in 2014 – struggled to match Williams both physically and technically and found herself a break down in the opening game of the second set.
The 25-year-old had her moments in the second set, but couldn’t capitalise on a series of break points in the fourth game and soon found herself languishing at 3-1 down.
The near scare seemed to spark Williams back into life, and she found another break to put the game beyond her opponent’s reach.
Williams will now face fellow American Madison Keys for a place in the final after the teenager defeated Venus Williams in today’s earlier quarter-final.