Ivanovic brushed off an early wobble to comfortably beat Kurumi Nara 6-2 6-3 in 76 minutes.
"Obviously I'm very thrilled to be through to the semi-finals," said Ivanovic.
"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."
Williams dispatched of Spain’s Garbine Muguruza 6-3 6-3 to book a semi-final meeting against fifth seed Jamie Hampton, who reached the last four courtesy of a 6-4 2-6 6-4 win over fellow American Lauren Davis.
In the Shenzhen Open, top seed Li Na stayed on course to start 2014 with a trophy after a hard fought 7-5 4-6 6-4 victory over Monica Niculescu.
Elsewhere, there were wins for fifth seed Shuai Peng and eighth seed Annika Beck.
Results - ASB Classic
Venus Williams beat Garbine Muguruza Blanco 6-3 6-3
2-Ana Ivanovic beat Kurumi Nara 6-2 6-3
3-Kirsten Flipkens beat Sachie Ishizu 6-4 7-5
Results - Shenzhen Open
8-Annika Beck beat Patricia Mayr-Achleitner 3-6 6-3 6-1
Vania King beat Barbora Zahlavova Strycova 6-2 6-4
1-Li Na beat Monica Niculescu 7-5 4-6 6-4
5-Peng Shuai beat Jana Cepelova 6-3 6-2