Narang, who won the bronze in 10m Rifle at the London Olympics, shot 185.8 overall to secure third place behind gold medallist Michael McPhail (208.8 points) of USA and Ole Kristian Bryhn (206.3) of Norway.
The other quota place from the event went to McPhail.
Earlier in the competition, Narang and India's only individual Olympic gold medallist Abhinav Bindra, had failed to qualify for the 10m Rifle final.
Chandela had secured the quota place by winning the bronze in the 10m Rifle at World Cup in Korea last month.
Pistol ace Jitu Rai had won India's first Olympic quota place at the World Championships in Granada, Spain last year, when he won silver in the 50m Free Pistol event.
Each country can win a maximum of 30 quota places from a total of 15 shooting disciplines (including shotgun events), two each from each discipline.