Jankovic, the seventh seed, took less than 90 minutes to seal a 6-4 6-3 win over Krunic, who made six double faults and was broken twice in the opening set.
"She (Krunic) is a player who is very talented and I've known her a long time," Jankovic told reporters. "I used to be her mentor and now I play against her. It's amazing to see her grow up and come to this stage.
"I don't like to play against someone who is my friend. It's never easy. I prefer to play someone else, but she played really well."
Jankovic will take on either Venus Williams or Alize Cornet of France in the next round.
Angelique Kerber, the world number one who lost to Jankovic in last year's final, won the first set against American Louisa Chirico but lost the second. The German was leading 2-1 in the third with play scheduled to resume on Thursday.
Australian Daria Gavrilova, the eighth seed, was leading 6-2 1-0 against unseeded Katerina Siniakova of the Czech Republic.
(Reporting by Ian Rodricks in Bengaluru; Editing by Ken Ferris)
