Bouchard called the Russian "a cheater" last week and suggested she should have been banned for life -- rather than 15 months -- after testing positive for meldonium at the 2015 Australian Open.
And the Canadian said she would have "a bit more motivation" against her former idol Sharapova after registering a first win on the WTA Tour since January against Alize Cornet on Saturday to set up the grudge match.
"I love being quiet about it and letting everyone around speak or have the noise."
Despite the controversy surrounding the decision to hand her a wildcard, Sharapova was given a warm reception by the sparse crowd on the main Manolo Santana court in the Spanish capital.
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"There's kind of an eeriness about the tournament," added Sharapova.
"You know the VIP tents are full, but then the courts don't always get the spectators in from the beginning of the match."
There were four breaks of serve in the opening six games, but Lucic-Baroni was good value for her lead when she served to take the first set.
Former number one Sharapova bounced back at the start of a gruelling second set that lasted over an hour by moving 4-1 in front.
However, Lucic-Baroni held off four set points and then broke back for 5-4.
And there was no stopping the five-time Grand Slam champion in the decider as she dismissed a dispirited Lucic- Baroni for the loss of just 11 points.
World number two Angelique Kerber eased into round two with a convincing 6-4, 6-2 win over Hungary's Timea Babos.
The German is the top seed in the draw with world number one Serena Williams absent because the 23-time Grand Slam champion is expecting her first child.
Kerber's form has been inconsistent this season, but she was rarely troubled in wrapping up victory in just over an hour on court.
Eighth seed and 2015 finalist in Madrid, Svetlana Kuznetsova, cruised past Yaroslava Shvedova 6-4, 6-3.
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