The 13th-seeded Ivanovic was ahead 6-1, 4-1 when Spain's Carla Suarez Navarro retired because of a right hip injury, while the 14th-seeded Kuznetsova also knocked out a Spaniard with a 7-5, 6-3 triumph over Maria Jose Martinez Sanchez. Kuznetsova was the Doha runner-up in 2004 and 2007.
Ivanovic and Kuznetsova, each former French Open champions, are two of the five Grand Slam champions in this week's field. Victoria Azarenka, coming off her first major championship at the Australian Open, is this week's top seed, while other Grand Slam winners scheduled to play this week are former French champ Francesca Schiavone and reigning U.S. Open winner Samantha Stosur.
The top eight seeds -- Azarenka, Caroline Wozniacki, Stosur, Agnieszka Radwanska, Marion Bartoli, defending Doha champion Vera Zvonareva, Schiavone and Jelena Jankovic -- all have byes into the second round. Zvonareva, also the Doha runner-up in 2010, beat Wozniacki for last year's title.
There was just one other seeded winner Monday, as China's Peng Shuai -- the 12th seed -- notched a 6-0, 7-5 victory over wild card Fatma Al Nabhani. Russia's Anastasia Pavlyuchenkova, the 10th seed, was handed an early exit by Kazakhstan's Ksenia Pervak, 1-6, 6-2, 6-3.
American Christina McHale also advanced with a 6-4, 6-3 win over South Africa's Chanelle Scheepers, while Bulgaria's Tsvetana Pironkova notched a 6-0, 6-4 victory over Slovenia's Polana Hercog.
The 2012 champion will earn a first prize of $385,000.