The No.2-seeded Ivanovic was the first of the two to advance, coming back from a break down in the first set and eventually cruising against Kurumi Nara in straight sets in an hour and 16 minutes, 62 63.
"Obviously I'm very thrilled to be through to the semifinals," Ivanovic said. "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."
Ivanovic needed only 43 minutes to win her previous round the day before, but it's hard to compare.
"It's hard to compare because it's a different kind of opponent, but I definitely did make some more errors today compared to yesterday," Ivanovic said. "Yesterday I played an almost perfect match."
Next up for Ivanovic is No.3 seed Kirsten Flipkens, who edged Japanese qualifier Sachie Ishizu in a tight two-setter, 64 75. Ishizu had her chances in both sets - she led 2-0 in the first set and 5-2 in the second set, even holding double set point at 5-4 in that second set - but Flipkens got out of it.
Flipkens beat Ivanovic in their only previous meeting, though it came on indoor hardcourts.
"It's always tricky playing your friend, but it's just a tennis match, so we go on court, we play our best, and we can have dinner afterwards," Ivanovic said. "We've practiced quite a few times and we played an exhibition in December, so it's definitely going to be fun playing her. I'm looking forward to it."
The Serbian-Belgian pair aren't just friends, they've also been playing doubles together this week - but after winning their singles quarterfinals they lost in the doubles quarterfinals, winning the first set but falling in a match tie-break against No.3 seeds Lucie Hradecka and Michaella Krajicek, 36 64 103.
Hampton and Williams will be playing against each other for the first time.