The French Open champion won 6-4, 7-6 to reach the Kremlin Cup final for the second year in a row.
U.S. Open champion Svetlana Kuznetsova beat Australian Samantha Stosur 6-4, 6-4 to reach the quarter-finals.
Svetlana Kuznetsova powered to her first Grand Slam title by beating fellow Russian Elena Dementieva 6-3, 7-5 in the final of the U.S. Open.
The French Open champion outlasted fellow Russian Vera Zvonareva in a thriller at the Acura Classic.
The teenager stunned champion Serena Williams 6-1 6-4 in the Wimbledon final to become the first Russian to win a singles title at the championships.
Serena was beaten by Jennifer Capriati while Venus lost to Russia's Anastasia Myskina in the women's quarter-finals at the French Open.
The world number one overcame Nathalie Dechy, while Jennifer Capriati beat Silvia Farina Elia at the Qatar Open.
Maria Sharapova powered into the semi-final with a 6-3, 6-3 defeat of Russian rival Anastasia Myskina at the Nasdaq-100 Open
Marat Safin paid the price for his later-than-scheduled arrival at the Hopman Cup as top seeds Russia suffered a shock defeat to Germany.
Following Iga Swiatek's victory over Coco Gauff in the final, here's a list of French Open women's singles champions:
Maria Sharapova has pulled out of Russia's Fed Cup semi-final against Germany in Sochi this weekend with a leg injury, the Russian Tennis Federation said on Tuesday.
By losing, Ostapenko joins a ignominious group including, as well as Myskina, Steffi Graf, Jennifer Capriati, Svetlana Kuznetsova and Angelique Kerber who all lost as Grand Slam champions on the first run of their defences.
Rafael Nadal returns to his favourite tournament, albeit not his preferred court, to begin pursuit of a record-extending 10th French Open title on Monday against Frenchman Benoit Paire.
Images from Day 2 of the French Open in Paris on Monday.
List of French Open women's singles champions:
List of French Open women's singles champions
Simona Halep became the first Romanian in 40 years to lift the French Open trophy at Roland Garros on Saturday.
Jelena Ostapenko became only the sixth female Grand Slam champion to lose in the opening round of their title defence on Sunday when she lost to Kateryna Kozlova at the French Open.
List of French Open women's singles champions
In an interview with rediff.com's Bikash Mohapatra, Ivanovic talks about her success, those 'disappointing' years in between and her future expectations.