Belgian fourth seed Clijsters, who made her return to tennis at this event last year ahead of her second Grand Slam title at the US Open, ousted Italy's Flavia Pennetta 7-6 (8/6), 6-4, to book a semi-final date with Ivanovic.
Clijsters, who had taken a two-year break to start a family, fired seven aces and connected on 67 percent of her first serves but the Italian would not go out easily, saving 11 of 14 break-point chances by Clijsters.
"There are moments when it's good, moments when it's not good," she said. "Each match has gone better. That's what I'm looking for."
Serbia's Ivanovic dominated without facing a break point in a 6-1, 6-3 triumph over 114th-ranked qualifier Akgul Amanmuradova of Uzbekistan that lasted just 56 minutes at the two million-dollar hardcourt event.
The 26-year-old Uzbek had ousted Serbian top seed Jelena Jankovic on Thursday.
Russian star Maria Sharapova eliminated France's Marion Bartoli 6-1, 6-4 to reach a Saturday semi-final against Russian teen Anastasia Pavlyuchenkova, who outlasted Belgium's Yanina Wickmayer 7-5, 3-6, 6-1.
It was the ninth match triumph in a row for the Russian, who is coming off a title at Istanbul and rallied after losing five of the first six games in the match for the triumph.
"I started off really well in the first set, got really tired after that and she came back and put up a great fight," Wickmayer said.
Sharapova has lost only one set this week. She surged ahead 5-0 with the aid of eight unforced errors from Bartoli and was never threatened.
Source: AFP American Edition