The 2012 champion was outplayed in the first set but came back to eventually beat the 20-year-old 4-6, 7-5, 6-2.
Sharapova, 27, claimed she was unsurprised that Bouchard flew out of the traps but knew she could take control once the 18th seed began to fade.
“Sometimes when you play someone who hasn’t been in that situation they can play loose and play really well like my opponent today so sometimes you have to wait for them to slow down,” Sharapova said.
“She played an unbelievable match, her level was extremely high and I am just very lucky to be the winner today.
“I would prefer to win in two sets but she started so well. I have had some very tough matches but you put all the work in so that you feel fresh after three sets.”
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BIOGRAPHY: Ethan Hazard
BIOGRAPHY: Daniel Sturridge