Having beaten Roberta Vinci in her first match after a 15-month doping ban on Wednesday, Sharapova reigned supreme over Makarova, edging the first set 7-5 before cruising the second 6-1.
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"I settled down a bit (compared to Wednesday). I executed a great plan today and I was really glad I pulled that off," Sharapova told reporters.
"Practicing is so different to matches, you cannot compare it. You just have to trust the work you have put in. It's great to come out and play matches. Being in the quarter-finals again is special."
Sharapova received a wild card for the tournament, having lost all her ranking points in the wake of her suspension, and she has also been invited to play in Madrid and Rome - moves that have angered some players.
Elsewhere, Johanna Konta suffered a straight-sets defeat to world number 26 Anastasija Sevastova, denying her a reunion with Simona Halep after their controversial Fed Cup meeting.
The British number one, who is largely untested on clay at the top level, lost a scrappy encounter 6-3 7-5.
Laura Siegemund defeated Svetlana Kuznetsova 6-4 6-3, while Carla Suarez-Navarro comfortably beat Elena Vesnina 6-2 6-4.
With additional reporting from Reuters
Read the original article on Eurosport: Sharapova marches on in Stuttgart as Konta falls to Sevastova