The 25-year-old Hingis placed her Czech opponent under intense pressure throughout the match and required three match points before Koukalova netted a forehand after 70 minutes."We were both pretty flat towards the end. I just had more to give," said Hingis.
"At the third match point, I was like 'thank God' it was over. The anticipation is coming back and every set I'm shaking off the rustiness of the last few years."
Hingis said her younger opponents did not know what to expect when they played her.
"They haven't seen me around for three years and they don't know what to expect," said Hingis. "Maybe that's one of the reasons and the other is they don't know me.
"One thing I realise is that some of the girls, they do have respect and when I see them I have to take advantage of it."
Looking ahead to her quarter-final, Hingis said: "I know she's a little girl so she's not going to overpower me.
"I don't think she really has a big weapon but neither does she have a weakness."