Wednesday's match was the Russian's first since losing to Serena Williams in the quarterfinals of the 2016 Australian Open, and her first match on clay in nearly two years.
Against the 36th-ranked Italian, Sharapova had a shaky start, conceding seven of the first eight points and dropping the opening two games within five minutes.
She finally took her fifth chance in the third game to break Vinci's serve.
Apart from producing a string of unforced errors, Sharapova also showed flashes of her old self - with several outstanding returns and cross-court winners, mostly followed by her trademark fist pump.
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When Vinci held serve to go 5-4 up, the Italian had already won more games than in her two previous matches, both two-set defeats, against Sharapova.
The Russian, however, broke again and converted her second set point with a forehand winner to take the opener.
Sharapova took control of the second set after an early break and held off three break points in her following service game.
She dropped only two points on serve in the rest of the match and closed out the win on Vinci's serve.
Last year, Sharapova tested positive for the banned substance meldonium. She had her initial two-year ban reduced to 15 months by the Court of Arbitration for Sport, which ruled that the Russian bore "less than significant fault" in the case and that she could not "be considered to be an intentional doper."
Sharapova had been taking meldonium for many years, but overlooked an announcement by the World Anti-Doping Agency that it added the drug to its banned list on Jan. 1, 2016.
As a result of the suspension, Sharapova lost her ranking. But the three-time winner from 2012-14 was given direct entrance to the main draw of the Stuttgart event. Organizers in Madrid and Rome followed the example and handed her a wild card for their events in May as well.
Several players, including Vinci, have criticized the invitation for a player who has been caught doping.
Earlier Wednesday, Sharapova completed a one-hour training session on an empty center court. Because her suspension ended only at midnight, she had not been allowed to use official tournament facilities before, forcing her to visit a local tennis club in Stuttgart for training since last weekend.
Sharapova next plays fellow Russian Ekaterina Makarova, who upset the seventh-seeded Agnieszka Radwanska Tuesday.
In other first-round play, Kristina Mladenovic beat Australian Open semifinalist Mirjana Lucic-Baroni 6-4, 6-2 to set up a second-round match against the top-seeded defending champion, Angelique Kerber. Sixth-seeded Johanna Konta defeated Naomi Osaka 7-6 (5), 3-6, 6-1, while Carla Suarez-Navarro and Elena Vesnina also advance.
Simona Halep became the first player to reach the quarterfinals after beating Barbora Strycova 6-2, 6-3.
