The seventh seeded Serbian needed an hour and four minutes to beat the 20-year-old Indian ace 6-1, 6-4 in a second round match on court No 1.
It was an easy victory for Ivanovic once she broke Sania in the second game of the first set.
Another break in the sixth game sufficed to give the Serbian the set.
Games went with serve till the eighth game in the second set, but Ivanovic changed tactics in the ninth and repeatedly used both flanks as she had done in the first set and made the Indian run from end to end. She broke and then held serve in the tenth to wrap the match.
Ivanovic's serve was a revelation and Sania never came close to threatening it. The 19-year-old Serbian dished out seven aces and converted three of the five break-points she forced to underline her authority.
Sania had beaten Alberta Brianti of Italy in the first round on Wednesday and advanced for the first time after two unsuccessful attempts.
She will team up with Frenchman Fabrice Santoro for the doubles competition.
But there was something to cheer about for Indian fans as Leander Paes and Martin Damm of the Czech Republic quelled the challenge of local hopes Jeremy Chardy and Jonathan Eysseric 7-6 (4), 7-6 (2) to advance into the second round of the men's doubles earlier.