Beijing Olympics gold-medallist Bindra finished seventh in the qualifying round to make the cut.
However, London Olympics bronze-medallist Narang missed out after finishing at a lowly 23rd position.
Bindra, who is taking part in his fifth and last Olympics, scored 625.7 to book a berth in the finals. This is the only event Bindra is competing in the ongoing Olympics.
Campriani Niccolo of Italy topped the qualification with a score of 630.2, which is an Olympic record.
Bindra, who crashed to a 16th place finish in 2012 London, scored 104.3, 104.4, 105.9, 103.8, 102.1 and 105.2.
His last series of 105.2 proved to be the clincher for Bindra, who raised his game when it mattered the most.
The final is slated later today.
Heena Sidhu, who bowed out of the 10m air pistol in the qualification round, will be seen in action tomorrow in 25m pistol.