The Russian, who was suspended last March after testing positive for meldonium, beat the Italian 7-5 6-3.
There was no noticeable bad reception for the 30-year-old, who responded well to losing her first service game to take a tight opening set in Stuttgart.
She broke twice in the second to progress to face Ekaterina Makarova.
Sharapova, who hit 11 aces and 39 winners, said: “I’ve been waiting for this for a long time.
“It’s the best feeling in the world, those first few seconds before you enter the arena. To know you were walking back out there was special.
“I spent a long time without hitting any balls. I didn’t know when I would be back. I went to school for a little bit, I grew my business and had a normal life. I put the racquet away for a little bit.
“I felt I had to grow as a person and I think I’ve done that. But this is what I’ve done for so long. I’m a competitor – that’s when I’m at my best.”
The decision to give five-time Grand Slam winner Sharapova a wildcard entry for this event, as well as upcoming tournaments in Madrid and Rome, has been questioned by a number of players, including her Italian first-round opponent.
However, it has been defended by WTA chief Steve Simon, who said it was in keeping with how former dopers were treated in other sports, adding that she was “starting at ground zero”.
The former world number one will find out on 16 May if she has been given a wildcard for the French Open, which starts on 28 May.
After Wednesday’s victory, the Russian told BBC Sport that she would “play in the juniors” if she had to, to compete at the French Open and Wimbledon in July.
