Double trap exponent Sangram clinched his first-ever senior medal in International Shooting Sport Federation tournament after years of toil, while Amanpreet bagged a well-deserved bronze after scoring 202.2 in the men's 50m pistol event.
Both shooters were taking part in the prestigious event for the first time.
"I am really happy as the hard training over the past three weeks has paid off," Sangram said after his effort.
Shooting alongside Amanpreet, the fancied Jitu, though, failed to impress and was the first to be eliminated at seventh place with a score of 123.2. Both had cleared the qualification hurdle without much fuss.
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In the double trap final at the Dr Karni Singh Shooting Ranges, Sangram shot 76 out of 80 targets, three behind gold medallist Hu Binyuan (79) of China.
Sangram had won a gold medal at the Asian Shooting Championship for junior way back in 2009.
Sangram shot exceedingly well throughout the day, first topping the qualifying with a score of 144 out of 150 and then replicating the showing in the final.
He could not overcome the world record effort of 2008 Olympic bronze medallist Hu Binyuan, who was in sublime form in the final.
India's world number one double trap shooter Ankur Mittal, who qualified for the six-man final in second position with a score of 139, finished fourth in the final.
Sangram's effort, somewhat, made up for the disappointment.
Amanpreet finished behind gold medallist Damir Mikec of Serbia and silver winner Oleh Omelchuk of Ukraine. Damir shot 229.3 and the Ukranian Omelchuk finished with a score of 228 in a thrilling round for the top prize.
In the qualifying round, Amanpreet had qualified in seventh spot, shooting 545 out of 600, while Jitu shot 561 to make the final in fourth position.
Amanpreet, who along with the rest of the Indian squad, will leave for Australia to take part in the Commonwealth Shooting Championship, said, "There was huge pressure shooting in front of the home crowd and I am really relieved.
"Considering that this is a World Cup Final with the best shooters in the fray, you can call this as my finest performance in shooting. I'm happy but score wise it's not great, so I need to improve on that," a pleased Amanpreet added.
In the day's other two finals, Denmark's Torben Grimmel won the men's 50m rifle prone with yet another world record score of 250.6 in the final. Germany's reigning Olympic champion Henri Junghaenel won silver with a score of 250.1 while Korea's Kim Jonghyun bagged the bronze with an effort of 228.7.
Both Kim and Zhang ended with 34 points each in the final after which Kim prevailed in a shoot-off. Zorana Arunovic of Serbia won the bronze.
Sangram and Amanpreet's effort took India to fourth in the medal standings with an overhaul haul of one gold, one silver and a bronze medal.