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The French Open champion started off strongly on the grass court by breaking her opponent's serve at the first time of asking.
Bacsinszky was able to salvage two break points in the fourth game of the opening set and grabbed a break of her own, but Sharapova took her opponent's serve a further two times to take a comfortable one-set lead.
Games initially went by way of serve in the second set, but once again, Sharapova comfortably nabbed a break to keep herself on top in the contest.
Another break of serve ensured that Sharapova was rarely troubled as she took the set and the match to progress into the next phase of the Grand Slam.