Sharapova plays a forehand to Voracova in Auckland (Photo: AP)
Third seed Svetlana Kuznetsova and the seventh to ninth seeds Elena Vesnina, Sofia Arvidsson and Carla Suarez Navarro all went out in the second round following sixth seed Kimiko Date-Krumm who lost her first match.
Sharapova had been expected to despatch Renata Voracova with ease but dropped her serve early to trail 1-3 before finding her rhythm to take out the first set 6-3.
A series of double faults in the second set saw her drop serve twice to be down 3-4, however her experience showed as she rallied again to take the set and the match 7-5.
"I'll definitely have to improve for the next one," said Sharapova who will play Greta Arn in the quarter-finals.
Arn dropped the first set in her second round match against Arvidsson but fought back for a 4-6, 7-5, 7-5 victory.
Wickmayer, the tournament defending champion, was also stretched to three sets to dispose of Sabine Lisicki 6-2, 3-6, 6-2.
At one-set all, Wickmayer said she knew she had to lift her game and after securing a service break early in the decider she was not troubled again.
"After the second set I knew I had to do something more to win the match otherwise I knew it was going to go the other way," Wickmayer said.
"I tried to be a lot more aggressive and lift my game, it wasn't that easy with the wind and maybe a risk in making more mistakes, but that's the game I wanted to play and I'm so happy now."
In the quarter-finals Wickmayer will play Romanian Simona Halep who beat Russian Vesnina.
Halep was leading 2-6, 6-4, 4-0 when Vesnina retired complaining of dizziness.
Third seed Kuznetsova, a two-time Grand Slam winner, blamed her inability to put away the big points for her loss to China's Peng Shuai in a three-set marathon that lasted more than two hours.
Kuznetsova won the first set 6-2, but Peng took the next two 6-4, 6-4.
"I was leading all the time, but when you don't take chances, the opponent will take them," Kuznetsova said.
"I felt like I was moving well, but at moments I didn't choose the right shot."