The top seed dominated the first set with a free-flowing game that oozed confidence as Hsieh, the daughter of a Taiwanese locksmith, just could not find the key to the Russian's armoury of powerful groundstrokes.
But Sharapova, who completed her career grand slam this month with victory in the French Open, then let her concentration slip.
Twice she lost her serve, clearly thrown by the swirling wind and delivered a string of double-faults much to her own fury.
Hsieh led 4-2 but could not maintain the pressure against Sharapova who clawed her way back. Hsieh saved two match points but lost the third when she sent a backhand wide.
The elegant Russian, who first won Wimbledon in 2004 at the age of 17, will have to sharpen her game against her next opponent, last year's semi-finalist Sabine Lisicki, the German beating American Sloane Stephens 7-6(5) 1-6 6-2.
"That's a tough one," Sharapova said. "She did extremely well last year. She is a very good player on grass and I look forward to it."
Kim Clijsters also reached the last 16 at Wimbledon when Russia's Vera Zvonareva was forced to retire through illness trailing 6-3 4-3 in their third-round match.
Belgian Clijsters, the former world number one who is playing her farewell Wimbledon, dominated the 12th seed who left the court for treatment after suffering breathing problems.
"I had to retire. It was not possible for me to play. You never want to retire during the grand slam, one of the great matches when you are playing a good player. It's never good," Zvonareva told reporters.
The 29-year-old Clijsters, Wimbledon semi-finalist in 2003 and 2006, controlled the match as Zvonareva, runner-up at the All England Club two years ago, made 28 unforced errors.
Clijsters, ranked 47th in the world, will play eighth seed Angelique Kerber in the last 16.
Kerber made short work of American 28th seed Christina McHale, rushing through 6-2 6-3 to continue her quiet progress through the tournament.
Shuai Peng was even more clinical, conceding just three games en route to a 6-1 6-2 victory over Arantxa Rus. Next up for the Chinese is Maria Kirilenko, who impressed against Sorana Cirstea to win through 6-3 6-1.