The top-seeded Russian, who will leapfrog Justine Henin-Hardenne to number two in the rankings if she reaches Sunday's final, showed little patience and made several careless errors against an enterprising opponent.
Daniilidou earned two break points to lead 4-2 but Sharapova held them off and then won a break to go 6-5 in front with a crosscourt backhand winner.
Sharapova had to survive another break point, saved with a backhand winner, before clinching the set with her seventh ace.
The U.S. Open champion broke Daniilidou from 40-0 to lead 1-0 in the second set and her opponent then called for medical attention for dizziness and a headache.
Having won five consecutive points, Sharapova then took six more before Daniilidou began to compete again.
But her challenge was muted and Sharapova broke to lead 4-1 with a winning return, and again for the match when a Daniilidou backhand volley fell wide.
"I thought she played really good solid tennis from the beginning. I don't think she made a lot of errors until 5-all," Sharapova told reporters.
"I thought I was playing well. I thought I was moving pretty well in the first set but she was obviously playing pretty good tennis and getting a lot of balls back no matter how hard or deep I hit.
"You've just got to keep steady and hope at some point with a bit of luck or patience your opponent will break down."
KNEE INJURY
Sharapova will next play fifth-seeded Serb Ana Ivanovic, who defeated Polish qualifier Agnieszka Radwanska 6-2, 6-2.
Ivanovic made a tentative start, allowing Radwanska to hold to love and then having to fend off three break points before she held for 1-1.
But then she snapped into gear, breaking for 2-1 with a blistering return, and after holding off a break point for 3-3 with her fourth ace of the match she broke again for 5-2.
Although Ivanovic was broken twice in the second set, Radwanska failed to hold her serve at all.
The biggest drama of the day occurred when twice grand slam champion Mary Pierce was carried off on a stretcher after collapsing on court with a right knee injury during her match against Russia's Vera Zvonareva.
Having saved three match points during the second set, Zvonareva was poised to take Pierce into a tiebreak when the Frenchwoman fell while running on the baseline.
Pierce immediately clutched her knee and screamed repeatedly as a startled Zvonareva, tournament officials and first aid staff rushed to assist.
The match was abandoned with Pierce leading 6-4, 6-6.
Third seed Patty Schnyder of Switzerland kept her slim hopes of qualifying for the WTA Championships alive with a 6-7, 6-4, 6-3 win over Frenchwoman Nathalie Dechy. Schnyder needs to reach the final in both Linz and in Hasselt next week to earn the final place in the eight-player Madrid field.
Seventh-seeded Anna Chakvtadze was upset 6-4, 6-4 by Australia's Samantha Stosur, while sixth-seeded Serb Jelena Jankovic advanced with a 6-7, 6-4, 6-2 win over Russian qualifier Elena Vesnina.
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