The Indian duo of Shushikala Agashe and Aleena Reji bagged the third spot after beating Korea in the third-fourth place race at the Indira Gandhi Indoor Stadium velodrome here.
The home team clocked 36.677 seconds while the Korea pair of Jeong Seolhwa and Ha Jieun clocked 36.735 seconds.
China then beat Chinese Taipei in the race for first and second places as the two teams clocked 35.819 seconds and 36.623 seconds respectively.
"We are proud to have won a medal for the country, but we are a bit disappointed as we could have done better and finished second in the qualification. That would have given us a chance to go for the gold or at least we would have won a silver," Aleena Reji told PTI after winning bronze.
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"However, we snatched the bronze medal from a tough opponent like Korea," said Aleena, who had also won a medal -- a silver -- in the Track Asia Cup held at the same venue here last year.
The two teams which finished first and second in the qualification compete for the gold medal while the third and fourth finishers in the qualification fight it out for the bronze.
Other Indians, however, failed to impress as they fell out of the medal bracket.
T Bidyaluxmi Devi did not finish owing to an injury in the women's elite 20km points race.
Indians failed to qualify for the finals in the junior men's and elite men's team sprint events as they finished seventh and eighth respectively in the qualification.
"Aleena is in the last year of competing among the juniors and under UCI (International Cycling Union) rules, she is allowed to take part among seniors. She and Deborah will take part in the team sprint event in the two World Cups in Cali in Colombia and Los Angeles in USA," he said.
Kazakhstan, China and Japan shared the spoils on the opening day by bagging two gold each.
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