The former French Open champion's competition is dwindling with American third seed Sloane Stephens and number four Kirsten Flipkens of Belgium ousted, 6-3 6-1 by China's Zhang Shuai and 6-4 6-2 by Czech Barbora Zahlavova Strycova respectively.
Ivanovic needed just 27 minutes to win the first set for the loss of one game as she capitalised on Koukalova's weak second serve.
The second set was a more even affair with the Czech momentarily leading 4-3 before Ivanovic reeled off the final three games to set up a semi-final with Shuai.
The Serbian has yet to drop a set in her three matches in the grasscourt tournament.
"I really tried to do my thing because I know she can be dangerous and last time we played, in Doha, I lost," Ivanovic said. "She's won on grass in the past and is a great competitor as she showed in her matches this week.
"I expected a tough match so from the first moment on I was trying to be really aggressive. 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," said Ivanovic.
The other semi-final pits Strycova against Australian Casey Dellacqua who beat 43-year-old Japanese Kimiko Date-Krumm 6-1 6-0.
Barbora Zahlavova Strycova (Czech Republic) beat 4-Kirsten Flipkens (Belgium) 6-4 6-2
16-Casey Dellacqua (Australia) beat Kimiko Date-Krumm (Japan) 6-1 6-0
1-Ana Ivanovic (Serbia) beat 6-Klara Koukalova (Czech Republic) 6-1 6-4
9-Zhang Shuai (China) beat 3-Sloane Stephens (U.S.) 6-3 6-1
- Sports & Recreation
- Zhang Shuai
- Sloane Stephens
- Kirsten Flipkens
- Barbora Zahlavova Strycova