Sharapova – who maintained her top 10 status in the WTA rankings with victory – will face Sara Errani in the semi-finals after the Italian eighth seed progressed when opponent Carlo Suarez Navarro retired in the third set.
The Russian pounced on her opponent’s shaky serve to edge a cagy opening set and used the momentum to coast into a 4-0 lead in the second and, despite some late Radwanska resistance, wrap up victory in one hour and 39 minutes.
"I think at the start I wasn't being smart at the right times and wasn't constructing the points well on my serve," said Sharapova.
"Obviously it was a very difficult end and she played extremely well on some of those match points. I was happy that I stayed aggressive and I was able to win the last one. It's a big win for me, probably the biggest since my injury."
WTA Stuttgart quarter-final results
5-Jelena Jankovic (Serbia) beat Alisa Kleybanova (Russia) 6-4 6-3
9-Ana Ivanovic (Serbia) beat Svetlana Kuznetsova (Russia) 6-3 2-6 6-4
8-Sara Errani (Italy) beat Carla Suarez Navarro (Spain) 6-3 6-7(6) 3-0 (Suarez retired)
6-Maria Sharapova (Russia) beat 1-Agnieszka Radwanska (Poland) 6-4 6-3
WTA Marrakech quarter-final results
Maria Teresa Torro (Spain) beat Polona Hercog (Slovenia) 7-6(3) 7-6(5)
1-Daniela Hantuchova (Slovakia) beat 6-Peng Shuai (China) walkover
Romina Oprandi (Switzerland) beat 3-Yvonne Meusburger (Austria) 6-4 6-4
5-Garbine Muguruza Blanco (Spain) beat Shahar Peer (Israel) 6-3 6-1
- Sports & Recreation
- Sara Errani
- WTA rankings
- Carla Suarez Navarro