Rhythm finished behind two former Olympic champions, gold medalists Anna Korakaki of Greece and silver medalist Olena Kostevich from Ukraine.
Rhythm’s effort warmed the hearts of Indians after Sarabjot Singh and Esha Singh both missed out on medals despite qualifying for the men’s and women’s 10m air pistol finals respectively.
On the day the ISSF returned to the Tokyo Olympics format, Rhythm shot 581 and Esha 579 in the 60-shot qualifying round to advance to the 24-shot Women’s Eight Finals in third and seventh place respectively.
A third Olympic champion in the finals field, Tokyo mixed team winner Jiang Ranxin of China led the pack with a 588, seven ahead of second-best Kim Bomi of Korea.
Ukraine legend Kostevych was the strongest of the blocks with a solid 10.6, but the Indians struggled early, especially Esha who started with three shots in the eight.
After 10 moves, Anna was in the lead with Olena behind her while Rhythm and Esha were in fifth and sixth.
By the end of the 20th however, when Esha had fallen and finished in sixth place, Rhythm was third and one point behind second placed Olena and 2.7 behind Anna.
She kept fighting but eventually stopped one point behind the Ukrainian with 219.1 on the board. Having established a good lead, Anna closed comfortably for gold with 241.3 while Olena shot 240.6 for silver.
It was also a breakthrough medal for Rhythm as it was his first senior individual medal in an Olympic discipline.
Divya TS, the third Indian in the running, shot 575 to finish in 17th place.