The Beijing Olympics gold medallist finished seventh in the qualifying round to make the cut.
However, London Olympics bronze medallist Gagan Narang was way off the mark and missed out of the finals 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 Games.
Bindra, who crashed to a 16th place finish in London four years ago, scored 104.3, 104.4, 105.9, 103.8, 102.1 and 105.2.
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His last series of 105.2 proved to be the clincher as he raised his game when it mattered the most.
Another seasoned campaigner Narang, however, disappointed after picking up 73.7 points from his first seven shots before firing a 10.8 to jump to the pole position with 105.3 points.
But he lost the plot in subsequent rounds. After scoring 105.3 in his first round, Narang's performance went downhill as he shot 104.5, 102.1, 103.4, 101.6, 104.8 in the next five to finish with 621.7 points in the field of 50 shooters.
Majhi just could not raise her level of marksmanship and lost the contest 1-7, losing three sets and drawing another.
Two other woman archers -- Deepika Kumari and L Bombayla Devi -- will take the field in individual elimination round of 32 clash on August 10.
The lone male archer Atanu Das is also set to be seen in action tomorrow.
Das showed fine composure and skill to bounce back from a poor start in his maiden Olympics to finish fifth in the qualification round. He will begin his elimination round against lowly 60th ranked Jitbahadur Muktan of Nepal.