Sharapova, bidding to win the tournament for a third year on the bounce, profited from her opponent’s shaky second serve to break five times en route to a 6-4 6-3 victory in one hour and 32 minutes.
The sixth seed needs to reach the semi-finals to retain her top 10 position in the WTA rankings.
The Pole's first serve was patchy, finding the box just 56 per cent of the time, but she was ruthless on the key points as she saved all three break points she faced and broke her opponent three times.
"Today was a pretty good match," said Radwanska. "I was playing very aggressively, serving not bad and moving okay on this surface. I think straight sets against someone who is playing very well on clay is a very good score."
Second seed Simona Halep is scheduled to face Svetlana Kuztentsova later on Thursday.
WTA Stuttgart second round results
6-Maria Sharapova (Russia) beat Anastasia Pavlyuchenkova (Russia) 6-4 6-3
1-Agnieszka Radwanska (Poland) beat Roberta Vinci (Italy) 6-3 6-2
- Sports & Recreation
- Roberta Vinci