The Russian world number two saved six break points in her first two service games before stepping up a gear to ease to victory in 66 minutes, finishing off the match with a sublime backhand topspin lob.
"I felt really good. It feels good to get back into action," she said.
"I think there's always room for improvement and hopefully I'll keep improving."
Daniilidou, who beat French Open champion Justine Henin-Hardenne of Belgium in the first round at Wimbledon, paid the penalty for failing to take her break-point opportunities as Sharapova grew in confidence.
The Greek contributed to her own downfall with seven double faults and her opponent took advantage to set up a second round clash with Dally Randriantefy of Madagascar.