A sparse crowd turned out to see the five-times grand slam winner begin her second tournament after completing a 15-month suspension for testing positive for banned substance meldonium and the Russian was made to work for the win by world number 20 Lucic-Baroni, who took the first set.
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.
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The 30-year-old Russian 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.
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Bouchard, 23, labelled Sharapova a "cheater" in an interview in April and said the WTA was setting a bad example to youngsters in letting her back into the sport.
"She's a cheater and ... I don't think a cheater in any sport should be allowed to play that sport again," she said.
"It's so unfair to all the other players who do it the right way and are true. I think from the WTA it sends the wrong message to young kids: 'cheat and we'll welcome you back with open arms'.
"I don't think that's right and (Sharapova is) definitely not someone I can say I look up to any more."
Bouchard beat Alize Cornet 6-4 4-6 6-1 on Saturday.
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