Asab defeated Tim Kneale of Great Britain by 30-27 margin in the bronze medal play-off match.
Asab was at his best in the play-offs as he didn't miss a single target en route to his medal.
Steven Scott of Great Britain won the gold, defeating China's Qiang Pan 27-25 in the final.
Asab had earlier qualified for the bronze medal match as the third best shooter in the semifinal round with a score of 28 out of 30.