Chenai and Shreyasi got the better of Lebanon 40-38 in the bronze-medal match to win India's fourth medal of the competition.
Kuwait's Abdulrahman Al Faihan and Sarah Al Hawal won gold in the event after beating the Korean pair of Oh Taekeun and Kang Geeeun 36-35.
The Indian pair had earlier in the day topped the 16-team qualification round with a combined score of 91.
Kynan shot 46 to Shreyasi's 45 to lead six pairs into the semi-final rounds.
Mixed team events in shooting including trap shooting are set to make a first appearance at the 2020 Tokyo Olympics as medal events and India will take a lot of encouragement from the results. This is the first year that the events are being played in world and continental level competitions.
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