Kirilenko cruised past qualifier Petra Martic 6-2, 6-1, and Ivanovic defeated Su-Wei Hsieh 6-1, 6-2 to advance to the second round.
In other matches, American qualifier Lauren Davis edged Svetlana Kuznetsova 3-6, 7-5, 7-5.
Ekaterina Makarova beat Anastasia Rodionova 6-1, 7-5, and Alize Cornet topped Elena Vesnina 6-3, 6-3.
Later Tuesday, Venus Williams will face Kristen Flipkens in her first match since May, when she lost in the first round of the French Open.
The 33-year-old Williams missed Wimbledon, after 16 consecutive appearances, because of a lower back injury.