Vinci expected "a lot of the crowd on Wednesday to be [cheering] for her".
Vinci had to work to save a number of break points in the third game but she was unable to prevent Sharapova breaking back and getting on the board for the first time.
Sharapova finished with 11 aces, 3 double faults, 39 winners, 21 unforced and she held her last nine service games. Her match against Vinci opens the Evening Session on Centre Court, where the eyes of the tennis world will be on what is a controversial comeback. "I've been waiting for this moment for a long time".
Sharapova, a former world No. 1 and five-time Grand Slam champion, wasn't allowed at the venue until the morning of the match.
Due to the suspension, Sharapova lost her ranking.
"Yes, you're rusty and you're trying to get the rhythm again", Sharapova said. "Sure, I think the wildcard should go to the people who can generate the most interest, someone who can actually make a run [in the tournament] or some of the best players available to a given tournament". "That's what I do". But the three-time victor from 2012-14 was given direct entrance to the main draw of the Stuttgart event. She will face Russia's Ekaterina Makarova in the second round Thursday.
Sharapova finished the first set with 24 winners to just six for Vinci.
Sharapova was suspended after testing positive for the banned substance meldonium at the 2016 Australian Open.
Sharapova's return isn't without controversy. The tennis world has been buzzing with speculation that the two-time victor would be forced to play qualifying matches - facing off against "rising" stars on side courts to actually earn a place in the main draw.
Giudicelli, who said he will discuss Sharapova's wildcard with French Open tournament director Guy Forget on 15 May, added: "The tournament is bigger than the players". The move, however, was not a surprising one as the event is sponsored by Porsche, one of the Russian's many high-profile personal sponsors.
A decision by the French Open on whether to give Sharapova a wild card is expected on 16 May. She has made over $300 million in endorsements and prize money, according to Forbes.