Kirilenko defeated Akgul Amanmuradova 6-3, 7-5 in a tough 2-hour, first-round match at the PTT Pattaya Open. Kirilenko won about two-thirds of the points on serve and dropped serve only once.
She also had a pair of breaks in each set while advancing.
Ivanovic was at 1-2 and about to serve the fourth game of the third set when play was suspended for the day because of rain. There had been a lengthy delay because of the weather earlier. Two other first-round matches will also need to be completed Wednesday.
Also No. 8-seeded Heather Watson advanced when, with Watson ahead 6-1, 3-0, Timea Babos retired.
Other players moving into the second round included Kimiko Date-Krumm, Nina Bratchikova, Anastasija Sevastova, Anastasia Rodionova and local wild-card entrant Luksika Kumkhum.
Celebrity Couples of 2014 [PHOTOS]