Narang finished second on the podium in the men's 50m rifle prone event and youngster Swapnil won bronze in the same event.
In the final, he shot 246.3 to end just 1.4 points adrift the leader and settled for the second place.
The experienced Annu Raj Singh secured the women's 25m pistol bronze.
On day three of competitions, India's medal hunt started when both Narang and Swapnil qualified for the eight-man final.
More From This Section
Sushil Ghalay, India's third contestant shot 614.1 to finish 10th among the 22 participants.
In the final, Swapnil was again the stronger to start with, briefly leading after the 10th shot, while Dane steered clear of the field after the 18th shot of the 24-shot final.
Narang and Swapnil continued to fight for the second and third places, before the former clinched it after the 22nd shot.
Dane registered a winning score of 247.7, Narang ended with 246.3 while Swapnil shot 225.6.
Narang knows that there is a lot of work to be done ahead of the 2018 Commonwealth Games.
"It was a test event for the Commonwealth Games next year and one of the things to test was the wind conditions and I did just that today. The final score still can be better and I know that I need to put in some more in that direction," he added.
Team-mate Rahi Sarnobat had the same score but finished third in qualifying on countback. Heena qualified in fifth place shooting 571.
In the final, Annu Raj called on all her experience to start the strongest in the field with a pair of perfect 5s in the first two five-shot series.
However, the Australian pair of Lalita Yauhleuskaya and Elena Galiabovitch were strong throughout to finish 1-2 with scores of 35 and 32 after the 10th and final series.
Heena finished fifth with a tally of 21, while Rahi ended sixth after shooting 17 in the final.
India have so far accumulated 10 medals in rifle and pistol from the Commonwealth Shooting Championships.