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 on www.wtatennis.com: "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.