Seeded number one in the absence of defending champion Yifan Hao of China, Humpy had no problems crushing Ayah Moaataz of Egypt while Harika survived a scare before turning the tables on Tatev Abrahamyan of United States.
The only other Indian in the fray - Mary Ann Gomes also got off to a good start as she held highly regarded Tatiana Kosintseva of Russia to a hard-fought draw.
The players will come back for the return game in the 64-players championship being played on a knockout bases.
Humpy won with white pieces as Moaataz was no match against the highest rated here. It was a Queen pawn opening wherein Humpy punished a reckless opening easily, winning a pawn first and then a piece to romp home easily.
Harika was under pressure for a long time against Abrahamyan. The French defense by Harika as black met with the Tarrasch variation and Harika felt the heat in a passive position when white had a huge spatial advantage.
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