The former World number one, who has been handed wildcard for the tournament, recovered from losing her first service game to register a 7-5, 6-3 win over Vinci in a thrilling first-round contest.
With the win, Sharapova has now set up a second-round encounter against Russia's Ekaterina Makarova, who clinched a 6-2, 6-4 win over Polish star Agnieszka Radwanska.
"I think it's one of the greatest gifts that a woman can receive in life, it's a blessing. It's a beautiful chapter in her life," Sport24 quoted Sharapova as saying when asked about Williams.
Williams, the 23-time Grand Slam champion, revealed last week that she is expecting her first baby and will not play again this year.
Wednesday's match was Sharapova's first since her quarter-final defeat to World number one Serena Williams at the 2016 Australian Open, where she was tested positive for banned substance Meldonium.
Meanwhile, the five-time Grand Slam champion has also been handed wild cards for
Whether Sharapova will receive a wildcard at Roland Garros will be known just a week before qualifying begins for the second major of the season, which is slated to be held from May 28 to June 11.
Earlier this month, French Tennis Federation (FFT) president Bernard Giudicelli had hinted at their reservations to give the 30-year-old player a wild card entry which she would require as her world ranking has almost disappeared during her absence.
Sharapova's initial two-year ban was earlier reduced to 15 months following an appeal to the court of arbitration for sport, which concluded she had not intended to cheat.
