Sharapova, winner of the tournament in 2014 and a semi-finalist last week in the Stuttgart Grand Prix, regained composure to take the second before blitzing the tired Lucic-Baroni in the third without dropping a game.
Sharapova will meet Bouchard, ranked 60, on Monday in an eagerly anticipated game due to the Canadian's fierce criticism of the WTA's decision to allow the Russian to return to competitive tennis.
Bouchard, 23, labelled Sharapova a "cheater" in an interview with Istanbul-based TRT World in April and said the WTA was setting a bad example to youngsters in letting her back into the sport.
(Reporting by Richard Martin; Editing by Toby Davis)
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