Having lost their last meeting at Doha earlier this year, Ivanovic came out swinging this time, storming through the first set in just 27 minutes, 6-1, and then breaking to go up 3-2 in the second set. The No.6-seeded Koukalova broke back and then held to go up 4-3, but the No.1-seeded Ivanovic made one more push, reeling off three games in a row to move comfortably into the semifinals, 6-1, 6-4.
"I expected a tough match so from the first moment on I was trying to be really aggressive," Ivanovic said. "I tried to dominate her and put pressure on her, and I played really well in that first set.
"The second set was a lot tougher. She's a tough competitor. I'm really happy to win in two sets."
Ivanovic came into her quarterfinal match tied with Carla Suárez Navarro for most WTA-level match wins on the year with 34, but has now separated herself from the Spaniard with her milestone 35th.
Other than that it has always taken her until October to reach 35 (2006, 2008, 2012 and 2013).
Ivanovic beat Zhang in the pair's only previous meeting, though it was almost three years ago.
Dellacqua beat Zahlavova Strycova in their only previous meeting, though that was two years ago.
Zhang, Zahlavova Strycova and Dellacqua are all tied together in one stat - they will all be playing the biggest semifinals of their careers, all of them playing their first Premier-level semifinals.
Meanwhile, Ivanovic is in her 30th semifinal at the Premier-level or above (10-19 in first 29).