The 28-year-old Sidhu shot a final score of 38, two of them perfect fives, to claim the top honours ahead of Australian Elena Galiabovitch.
This was her second medal at the 2st Games after having claimed the silver in the 10m air pistol event behind 16-year-old compatriot Manu Bhaker.
Earlier, defending silver-medallist Gagan Narang signed off a disappointing seventh while debutant Chain Singh finished fourth in the 50m rifle prone event at the Belmont Shooting Centre.
Narang, who qualified third for the final with a score of 619.4, went out after the first stage of elimination.