The $3 million season-ending tournament, now in its second day in the Spanish capital, brings together the eight top-ranked women.
Fourth-seeded Ivanovic, playing on her 20th birthday, beat second-seeded Kuznetsova 6-1, 4-6, 7-5.
Also on Tuesday, Russia's Maria Sharapova (seeded 6) defeated Daniela Hantuchova (8) of Slovakia in straight sets, 6-4, 7-5.
The latest young Russian tennis star to enter top 10 this year, Anna Chakvetadze (7), lost to World No. 1 Justine Henin of Belgium, 1-6, 6-7.
On Wednesday's matches Ivanovic will face Hantuchova, Henin will play world No. 2 Jelena Jankovic (3) of Serbia and Chakvetadze will take on Serena Williams (5) of the United States.