World No 1 and defending champion Williams saw off ninth seed Dominika Cibulkova in straight sets, beating the Slovakian 6-3, 6-3, but Sharapova was made to work a little harder by Kaia Kanepi for her victory.
Estonian Kanepi, the 2012 winner, took the first set and was a break up in the second, but Sharapova battled back to claim the match 4-6, 6-3, 6-2.
A relieved Sharapova said: “She’s (Kanepi) a really tough opponent. For me it was a slow start. I wasn’t very sharp in the beginning. I’m happy I pulled it through, and at this stage it’s a good match for me to get through.”
Sharapova has her work cut out to make it through to the final as she has lost 14 of her 16 career meetings with Williams – including all of their last 13 encounters.
The Russian added: “I haven’t had a lot of success against her in the past. But it’s the first tournament of the year. You always hope that you can go out and give yourself a chance to do better next time.”
The other semi-final will see second seed Victoria Azarenka play Jelena Jankovic, the fourth seed.
Both players were taken to deciding sets by their last-eight opponents before going through, with Azarenka defeating Stefanie Voegele 6-4, 6-7 (7/9), 6-1, while Jankovic battled back from a set down to beat fifth-seeded Angelique Kerber 6-7 (8/10), 6-3, 6-1.
In Auckland, New Zealand, second seed Ana Ivanovic brushed aside the challenge of Kurumi Nara to seal her spot in the semi-finals of the ASB Classic and a showdown with doubles partner Kirsten Flipkens.
The Serbian recovered from a break down in the first set to beat her Japanese opponent 6-2, 6-3 in an hour and 16 minutes.
Ivanovic said after her victory: “Obviously I’m very thrilled to be through to the semi-finals.
“It was a really tough match. The score doesn’t really indicate how close it was. I was really surprised by her game – she played really well today, I thought. But I was really happy I managed to close it out in straight sets.” Next up for Ivanovic is Belgian third seed Flipkens, who eased past another Japanese player, qualifier Sachie Ishizu, 6-4, 7-5.
Ivanovic and Flipkens are good friends and have also competed in the doubles in Auckland, where they were beaten at the quarter-final stage by Lucie Hradecka and Michaella Krajicek.
The other semi-final pits Venus Williams against her fellow American Jamie Hampton.
Williams had few problems seeing off Spaniard Garbine Muguruza 6-3, 6-3, but fifth seed Hampton was taken the distance by compatriot Lauren Davis before recording a 6-2, 4-6, 6-4 triumph.
Top seed Li Na stayed on course to make a successful defence of her Shenzhen Open title as China’s leading player came through a tough quarter-final.
The 31-year-old former French Open champion and current world number three was pushed to three sets by Romanian Monica Niculescu, who had won their only previous match, played in Beijing during 2011.
Li edged the decider to earn a 7-5, 4-6, 6-4 victory over 59th-ranked Niculescu, setting up a semi-final against Germany’s Annika Beck.
In the final match of the day, Beck was in trouble early on against Austrian Patricia Mayr-Achleitner before scrapping for a 3-6, 6-3, 6-1 victory.
There could be an all-Chinese final tomorrow as Shuai Peng is through to the semi-finals. after beating Slovakian Jana Cepelova 6-3, 6-2.