The Russian eased to a 7-5 6-2 victory against her Romanian opponent, ranked 334th in the world, to reach the second round where she will play American world number 55 Christina McHale, who beat Shuai Peng of China, on the clay.
One-time world number 26 Dulgheru, 23, has suffered from injuries in recent years. She managed to break Sharapova once in the first set, but the world number two broke twice herself then raced into a 4-1 lead in the second set and closed it out from there.
Sharapova, 24, had won their only previous meeting in the Miami quarter-finals in 2011.
WTA Madrid results
Laura Robson (Britain) beat 4-Agnieszka Radwanska (Poland) 6-3 6-1
7-Sara Errani (Italy) beat Sorana Cirstea (Romania) 7-5 2-6 6-4
6-Angelique Kerber (Germany) beat Alize Cornet (France) 6-4 6-2
2-Maria Sharapova (Russia) beat Alexandra Dulgheru (Romania) 7-5 6-2
Christina Mchale (U.S.) beat Peng Shuai (China) 7-5 5-7 6-1
Carla Suarez Navarro (Spain) beat 9-Samantha Stosur (Australia) 7-6(7) 6-2
Kristina Mladenovic (France) beat Silvia Soler Espinosa (Spain) 6-1 6-1
3-Victoria Azarenka (Belarus) beat Anastasia Pavlyuchenkova (Russia) 7-6(8) 7-6(3)
- Sports & Recreation