Bouchard called Sharapova "a cheater" last week and was also critical of the Russian's welcome back to the sport after a 15-month doping ban with a series of wildcards for big events.
The world number 60 admitted she was extra motivated to face her former idol and it showed as she showed signs of the form she has lost over the past few years since reaching the Wimbledon final in 2014 in a bruising near three-hour contest.
However, adversity brought out the best in the five-time Grand Slam champion as Sharapova found the precision to match her power in the second set, reeling off four straight game from 2-2 to level at one set all.
Both players struggled to hold serve in the deciding set as a total of 14 break points were squandered.
However, Bouchard held her nerve when serving for the match at 5-4 as she saw off two break points and an unfortunate let cord on her first match point.
Bouchard will face top seed Angelique Kerber, who fought back from 5-3 down in the deciding set to overcome Katerina Siniakova 6-2, 1-6, 7-5 earlier on Monday, in the third round.
Kerber has had an inconsistent season and her fragile form was on show in the course of the first two sets.
The German romped through the opening set in 27 minutes but then had to save six break points for her only game in the second.
Siniakova served for the match at 5-4 in the deciding set, but Kerber should impressive fight to win the last four games.
In the men's Madrid Masters there were comfortable wins for Thomas Berdych, Grigor Dimitrov and Nick Kygios.
However, 15th seed Gael Monfils bowed out in a wild match against French compatriot Gilles Simon 0-6, 6-0, 7-6 (7/0).
Andy Murray begins his quest for a third title in Madrid on Wednesday when he faces Romanian Marius Copil.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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