Sharapova struggled at the start, which was perhaps to be expected, and her movement in particular was very sloppy.
However her service game quickly picked up and as the match wore on she clearly started to feel more relaxed.
The Russian's return to the sport after serving an 18 month ban has been met with a strong degree of criticism with a number of players saying they think it is not fair the way she has been welcomed back and given a wild card entry to Stuttgart.
Her reception as she walked out onto the card could probably best be described as lukewarm as there was a mixture of cheering and booing.
Vinci started well, winning her first service game before breaking Sharapova's first service game on her return.
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.
The pair served out until Sharapova produced a couple of huge returns and broke to go 6-5 up, winning the first set.
In the second Sharapova started much better, winning the first two games before Vinci eventually got on the board.
The longer it went on the more fluid Sharapova looked as she wrapped up her first win on her return, taking advantage of her serve which by now was in full flow as she record 11 aces in total.
Some fierce returning saw her break for the win, which resulted in a far more positive response from the crowd.
She will now face Ekaterina Makarova in the next round after her compatriot knocked Agnieszka Radwańska out.
The winner of that match could potentially face Garbiñe Muguruza in the quarter-finals.
Read the original article on Eurosport: Sharapova wins on return from ban