It was the third seed's third straight sets victory of the tournament but she looked in trouble when trailing 5-2 in the second set.
She then broke Ishizu twice to take the set and match in one hour 24 minutes. Flipkens was a beaten quarter-finalist at last year's ASB Classic.
Ivanovic and Flipkens were in action yesterday playing their doubles quarter-final against third seeds Lucie Hradecka and Michaella Krajicek.
Meanwhile, fifth seed Jamie Hampton won the all-American battle for the third semifinal spot, beating Lauren Davis in a marathon three-set battle.
The practice partners thrived while facing each other's serve throughout the match, with 12 breaks of serve among 30 break point opportunities across the three sets.
The final of those breaks proved decisive, with Hampton taking Davis' serve when the match seemed set for a tie-break, winning 6-2 4-6 6-4.
Hampton will now face the winner of last night's match between former world No1 Venus Williams and Spanish 20-year-old Garbine Muguruza. APNZ