Chinappa and Anaka Alankamony won their matches after India number one Pallikal lost the opening singles to Hong Kong's top player Annie Au in five gruelling games.
India, who had to settle for a bronze in Guangzhou four years ago, have a good chance winning the silver here.
Having beaten the fancied Hong Kong unit, they should beat Pakistan later in the day and China tomorrow on the way to topping the group. In that scenario, India are likely to face either Korea or Japan from the other group in the semifinals.
"We have a good chance for silver now but we are not thinking too far ahead. Hopefully we can top our pool and take it forward from there," World No.12 Pallikal told PTI.
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India's first ever women's singles bronze medallist at Asian Games went down fighting to 11th-ranked Annie 11-5 6-11 8-11 12-10 9-11, giving the opposition early advantage.
Pallikal's longtime teammate and Word No. 21 Chinappa had to win against 23rd-ranked Joey Chan to keep India alive in the tie.
She staged a remarkable recovery to keep her team afloat in the competition, coming back from two games down to win 6-11 8-11 11-5 11-9 11-9.
The Indian, whose ranking has dropped drastically in the last two years, played a solid match to give India an unexpected win. The final scoreline read 11-8 11-13 11-9 11-5 in favour of Alankamony.
Indian men's team led by singles silver medallist Saurav Ghosal will play their second pool match against China later today.