World No. 10 Indian, playing with black pieces, had to be at her defensive best to avoid conceding the game.
"I started the game quite well but played a miscalculated move which gave away my opponent the edge," Harika said after her match last night.
"I got into a good position in the dying moments of the game but couldn't convert and settled for a draw," she added.
She will take on English Grandmaster Nigel Short in her last game of the competition.