Narang, Bindra and Rajput combined for a score of 1783, a point adrift of gold medal winning Chinese team comprising Jikang Yu, Qinan Zhu and Yifei Cao.
Korea settled for the bronze in this event.
While Narang shot a score 597, Bindra and Rajput managed identical tallies of 593.
However, disappointment was in store for India in other events as the women's 10m air rifle team finished seventh and men's 50m pistol team could manage only a fifth place finish.
In the individual events, Commonwealth Games gold medallist Omkar Singh was the only among three Indians men's shooters to qualify for the final of 50m pistol event but eventually finished seventh.
In the women's individual events, Suma Shirur, Tejaswini Sawant and Kavita Yadav could not even qualify for the finals.
The same trio finished seventh in the women's 10m air rifle team event after totalling 1176 points.
The gold in this event went to hosts China while the silver was claimed by Iran. Uzbekistan settled for bronze at the Aoti shooting range.
The Chinese trio of Yi Siling, Wu Liuxi and Yu Dan totalled 1,194 points. The Iranian team managed a total of 1192, while Uzbekistan finished a distant third with 1182 points.
In the 50m pistol team event Omkar Singh, Amanpreet Singh and Deepak Sharma
finished fifth with a total of 1646 points.
South Korea bagged the gold medal in this event ahead of China, while Japan took the bronze.
The Korean team of Jin Jong-Oh, Lee Sang-Do and Lee Dae-Myung pulled off an overall tally of 1,679 points to beat the home trio of Pang Wei, Pu Qifeng and Wu Jing, who managed 1,671 points.
Japan finished with 1,667 points.
In the 10m air rifle women's individual event, veteran markswoman Suma shot a point better than her performance in last month's Delhi Commonwealth Games but still failed to qualify for the finals.
World record holder Suma shot 596 that included 33 perfect tens, with sequences of 98, 99, 100 and 99 and was edged out of the qualification ranks. She had shot 595 while winning the Team bronze with Kavita in the CWG.
Kavita, who finished 28th with 390 (96 98 98 98) had 27 perfect tens while Tejaswini, who is the world champion in 50m prone, also tallied the same with 24 Perfect tens to finish a distant 33rd from 54 shooters.
She started brilliantly with a 99 but then fell off to bring off scores of 98 98 and 95.
Kavita told PTI that this was only her third event after she made her debut in the World Championships.
"This is only my third event after the world championship. I am improving," said the Bangalore-based Kavita who took to the sport four years ago.
Asked about Tejeswini's poor show in an event that's not per favourite one, Kavita Said "it happens, it's just a game".
Omkar Singh, who won the 50m pistol individual gold in CWG, entered the final by finishing fifth in the qualifiers with 557 points. He later ended seventh in the final with a score of 648.2.