Hingis, the world No. 1, suffered a 6-2, 6-2 defeat at the hands of eighth seed Elena Dementieva of Russia.
Kafelnikov, however, snapped an eight-game losing streak against Thomas Johansson with a 6-3, 7-5 victory over the Swede.
This marks only the second time in her last nine tournaments that Hingis has been knocked out before the semifinals. The Swiss star endured a humiliating first-round exit at Wimbledon, falling to Spain's Virginia Ruano Pascual.
Hingis' loss continued the upset trend at Olympic Stadium. No. 2 Amelie Mauresmo of France and No. 3 Justine Henin of Belgium also suffered defeats Thursday, marking the first time three of the top four seeds have been eliminated from a Tier I WTA tournament.
Along with Mauresmo and Henin, No. 4 Nathalie Tauziat of France also had a first-round bye before saying a quick goodbye. The 1999 Kremlin Cup champion lost to Francesca Schiavone of Italy Wednesday.
Dementieva advanced to her second semifinal in as many weeks. Dementieva's victory sets up the first all-Russian semifinal in Kremlin Cup history. On Saturday, she will face compatriot Anastasia Myskina, who got past Austrian Barbara Schett, 6-4, 6-2.
Kafelnikov finally conquered his fiercest adversary. Johansson had won nine of 13 career meetings with the Russian prior to Friday's quarterfinal meeting.
Kafelnikov's next opponent will be No. 4 Tommy Haas of Germany, who disposed of Magnus Gustafsson of Sweden, 6-1, 6-4.
Ranked sixth in the ATP Champions Race, Kafelnikov has enjoyed considerably more success against Haas, winning four of their five lifetime meetings.
In the women's draw, No. 5 Jelena Dokic of Yugoslavia will clash with No. 7 Silvia Farina Elia of Italy in the other semifinal.
Dokic, who is gunning for her third WTA title of the year, routed another Italian, Francesca Schiavone, 6-2, 6-0. Farina Elia fought back from a one-set deficit and battled through a second-set tiebreak to overcome Daja Bedanova of the Czech Republic, 1-6, 7-6 (11-9), 6-4.
The other men's semifinal pits Dominik Hrbaty of Slovakia against Nicolas Kiefer of Germany.
Hrbaty, who rallied to defeat No. 2 Marat Safin of Russia on Thursday, battled back once again to beat Jiri Novak of the Czech Republic, 5-7, 6-4, 6-3. Kiefer got past two-time champion Marc Rosset of Switzerland, 6-3, 7-6 (7-1).